Dr McCulloch's research interests are computational methods for quantum many-body systems, specifically using Tensor Network methods. Dr McCulloch has made significant contributions to the field, especially in the realm of the one-dimensional version of Tensor Networks known as Matrix Product States (MPS). Dr McCulloch has 20 years of experience in developing sophisticated, high performance computational software and tools, and applying them to open problems in condensed matter and quantum physics.
Dr McCulloch has made many significant contributions to the development of numerical algorithms based on Tensor Networks, particularly the one-dimensional version known as the Density Matrix Renormalization Group (DMRG), and Matrix Product States (MPS). He has more than 20 years of experience in developing sophisticated, high performance computational software and tools, and applying them to open problems in condensed matter and quantum physics. He is the author of several papers as first or sole author which are now standard references in the field, with key contributions in how to incorporate symmetries into tensor networks, and new algorithms for excited states, translationally invariant systems, and frequency-space methods. Recent research themes include searching for candidate models of topologically ordered materials, non-equilibrium dynamics and thermalization, and quantum simulation.
Journal Article: Topological nature of spinons and holons: elementary excitations from matrix product states with conserved symmetries
Zauner-Stauber,, Vanderstraeten, L., Haegeman, J., McCulloch, I. P. and Verstraete, F. (2018) Topological nature of spinons and holons: elementary excitations from matrix product states with conserved symmetries. Physical Review B, 97 23: . doi:10.1103/PhysRevB.97.235155
Journal Article: Topological phase transition and the effect of Hubbard interactions on the one-dimensional topological Kondo insulator
Pillay, Jason C. and McCulloch, Ian P. (2018) Topological phase transition and the effect of Hubbard interactions on the one-dimensional topological Kondo insulator. Physical Review B, 97 20: . doi:10.1103/PhysRevB.97.205133
Journal Article: Phase diagram of the quantum Ising model with long-range interactions on an infinite-cylinder triangular lattice
Saadatmand, S. N., Bartlett, S. D. and McCulloch, I. P. (2018) Phase diagram of the quantum Ising model with long-range interactions on an infinite-cylinder triangular lattice. Physical Review B, 97 15: . doi:10.1103/PhysRevB.97.155116
Quantum thermodynamics of ultra-cold atoms
(2019–2021) ARC Discovery Projects
Simulating quantum states of matter: connecting theory to applications in science and technology.
(2015–2019) ARC Future Fellowships
Advanced Superfluid Physics Facility
(2015–2016) UQ Major Equipment and Infrastructure
Frustrated spin systems, an MPS approach
(2017) Doctor Philosophy
Many body localization and topological states in two dimensional quantum matter
Doctor Philosophy
Simulation of Stochastic Transport in Complex Systems Using Quantum Techniques
(2014) Master Philosophy
Tensor Network / Matrix Product State methods for computational quantum many-body problems
Tensor Networks provide a representation of a quantum many-body wave-function (or a classical partition function) that is suitable for computational methods, mainly for low-dimensional problems (1D and 2D). The most mature branch of tensor networks is known as Matrix Product States (MPS), often called DMRG. These days this is the widely used method to solve 1-dimensional quantum many-body problems. At UQ, we have developed the Matrix Product Toolkit, which is a comprehensive software toolkit for many kinds of MPS-based computations, including ground-states, real-time dynamics, and thermal and dissipative states. This software toolbox has been used in approximately 70 research publications in various fields of condensed matter and quantum science, ranging from ultra-cold atoms in optical lattices, ion traps, Josephson Junction arrays, strongly correlated systems, frustrated magnetism, topological order, dynamical mean-field theory. See my publications at ResearcherID for more details.
I am happy to talk to you to find a suitable project at any level, from summer project to PhD. Possible short projects would be, for example, learning about the Matrix Product Toolkit and trying some calculations (depending on the details and rate of progress this could lead to a research publication), or implementing a simple MPS or tensor network algorithm in Python or Matlab.
Possible PhD projects would be based around one of three possible themes:
Zauner-Stauber,, Vanderstraeten, L., Haegeman, J., McCulloch, I. P. and Verstraete, F. (2018) Topological nature of spinons and holons: elementary excitations from matrix product states with conserved symmetries. Physical Review B, 97 23: . doi:10.1103/PhysRevB.97.235155
Pillay, Jason C. and McCulloch, Ian P. (2018) Topological phase transition and the effect of Hubbard interactions on the one-dimensional topological Kondo insulator. Physical Review B, 97 20: . doi:10.1103/PhysRevB.97.205133
Saadatmand, S. N., Bartlett, S. D. and McCulloch, I. P. (2018) Phase diagram of the quantum Ising model with long-range interactions on an infinite-cylinder triangular lattice. Physical Review B, 97 15: . doi:10.1103/PhysRevB.97.155116
Symmetry between repulsive and attractive interactions in driven-dissipative Bose-Hubbard systems
Gangat, Adil A., McCulloch, Ian P. and Kao, Ying-Jer (2018) Symmetry between repulsive and attractive interactions in driven-dissipative Bose-Hubbard systems. Scientific Reports, 8 1: 3698. doi:10.1038/s41598-018-21845-5
Saadatmand, S. N. and McCulloch, I. P. (2017) Detection and characterization of symmetry-broken long-range orders in the spin-1/2 triangular Heisenberg model. Physical Review B, 96 7: . doi:10.1103/PhysRevB.96.075117
Precursor of the Laughlin state of hard-core bosons on a two-leg ladder
Petrescu, Alexandru, Piraud, Marie, Roux, Guillaume, McCulloch, I. P. and Le Hur, Karyn (2017) Precursor of the Laughlin state of hard-core bosons on a two-leg ladder. Physical Review B, 96 1: . doi:10.1103/PhysRevB.96.014524
Efficient perturbation theory to improve the density matrix renormalization group
Tirrito, Emanuele, Ran, Shi-Ju, Ferris, Andrew J., McCulloch, Ian P. and Lewenstein, Maciej (2017) Efficient perturbation theory to improve the density matrix renormalization group. Physical Review B: Condensed Matter and Materials Physics, 95 6: . doi:10.1103/PhysRevB.95.064110
Generic construction of efficient matrix product operators
Hubig, C., McCulloch, I. P. and Schollwock, U. (2017) Generic construction of efficient matrix product operators. Physical Review B, 95 3: . doi:10.1103/PhysRevB.95.035129
Prethermalization and persistent order in the absence of a thermal phase transition
Halimeh, Jad C., Zauner-Stauber, Valentin, McCulloch, Ian P., De Vega, Ines, Schollwock, Ulrich and Kastner, Michael (2017) Prethermalization and persistent order in the absence of a thermal phase transition. Physical Review B, 95 2: . doi:10.1103/PhysRevB.95.024302
Greschner, S., Piraud, M., Heidrich-Meisner, F., McCulloch, I. P., Schollwock, U. and Vekua, T. (2016) Symmetry-broken states in a system of interacting bosons on a two-leg ladder with a uniform Abelian gauge field. Physical Review A, 94 6: . doi:10.1103/PhysRevA.94.063628
Nourse, H. L., McCulloch, I. P., Janani, C. and Powell, B. J. (2016) Haldane insulator protected by reflection symmetry in the doped Hubbard model on the three-legged ladder. Physical Review B, 94 21: . doi:10.1103/PhysRevB.94.214418
Saadatmand, S. N. and McCulloch, I. P. (2016) Symmetry fractionalization in the topological phase of the spin-1/2 J(1)-J(2) triangular Heisenberg model. Physical Review B, 94 12: . doi:10.1103/PhysRevB.94.121111
Optical conductivity of the Hubbard chain away from half filling
Tiegel, Alexander C., Veness, Thomas, Dargel, Piet E., Honecker, Andreas, Pruschke, Thomas, McCulloch, Ian P. and Essler, Fabian H. L. (2016) Optical conductivity of the Hubbard chain away from half filling. Physical Review B: Condensed Matter and Materials Physics, 93 12: 125108-1-125108-5. doi:10.1103/PhysRevB.93.125108
Imaginary-time matrix product state impurity solver for dynamical mean-field theory
Wolf, F. Alexander, Go, Ara, McCulloch, Ian P., Millis, Andrew J. and Schollwoeck, Ulrich (2015) Imaginary-time matrix product state impurity solver for dynamical mean-field theory. Physical Review X, 5 4: . doi:10.1103/PhysRevX.5.041032
Greschner, S., Piraud, M., Heidrich-Meisner, F., McCulloch, I. P., Schollwock, U. and Vekua, T. (2015) Spontaneous increase of magnetic flux and chiral-current reversal in bosonic ladders: swimming against the tide. Physical Review Letters, 115 19: 1-5. doi:10.1103/PhysRevLett.115.190402
Chebyshev matrix product state approach for time evolution
Halimeh, Jad C., Kolley, Fabian and McCulloch, Ian P. (2015) Chebyshev matrix product state approach for time evolution. Physical Review B, 92 11: . doi:10.1103/PhysRevB.92.115130
Strongly interacting bosons on a three-leg ladder in the presence of a homogeneous flux
Kolley, F., Piraud, M., McCulloch, I.P., Schollwock, U. and Heidrich-Meisner, F. (2015) Strongly interacting bosons on a three-leg ladder in the presence of a homogeneous flux. New Journal of Physics, 17 9: . doi:10.1088/1367-2630/17/9/092001
Nonthermal Melting of Neel Order in the Hubbard Model
Balzer, Karsten, Wolf, F. Alexander, McCulloch, Ian P., Werner, Philipp and Eckstein, Martin (2015) Nonthermal Melting of Neel Order in the Hubbard Model. Physical Review X, 5 3: . doi:10.1103/PhysRevX.5.031039
Phase diagram of the spin-1/2 triangular J1-J2 Heisenberg model on a three-leg cylinder
Saadatmand, S. N., Powell, B. J. and McCulloch, I. P. (2015) Phase diagram of the spin-1/2 triangular J1-J2 Heisenberg model on a three-leg cylinder. Physical Review B (Condensed Matter and Materials Physics), 91 24: 245119.1-245119.11. doi:10.1103/PhysRevB.91.245119
Vortex and Meissner phases of strongly interacting bosons on a two-leg ladder
Piraud, M., Heidrich-Meisner, F., McCulloch, I. P., Greschner, S., Vekua, T. and Schollwöck, U. (2015) Vortex and Meissner phases of strongly interacting bosons on a two-leg ladder. Physical Review B - Condensed Matter and Materials Physics, 91 14: 140406.1-140406.5. doi:10.1103/PhysRevB.91.140406
Quantum critical spin-2 chain with emergent SU(3) symmetry
Chen, Pochung, Xue, Zhi-Long, McCulloch, I. P., Chung, Ming-Chiang, Huang, Chao-Chun and Yip, S. -K. (2015) Quantum critical spin-2 chain with emergent SU(3) symmetry. Physical Review Letters, 114 14: 145301.1-145301.5. doi:10.1103/PhysRevLett.114.145301
Strictly single-site DMRG algorithm with subspace expansion
Hubig, C., McCulloch, I. P., Schollwoeck, U. and Wolf, F. A. (2015) Strictly single-site DMRG algorithm with subspace expansion. Physical Review B, 91 15: 155115-155115. doi:10.1103/PhysRevB.91.155115
Spectral functions and time evolution from the Chebyshev recursion
Wolf, F. Alexander, Justiniano, Jorge A, Mcculloch, Ian P and Schollwock, Ulrich (2015) Spectral functions and time evolution from the Chebyshev recursion. Physical Review B - Condensed Matter and Materials Physics, 91 115144: 115144-1-115144-17. doi:10.1103/PhysRevB.91.115144
Fast convergence of imaginary time evolution tensor network algorithms by recycling the environment
Phien, Ho N., Mcculloch, Ian P. and Vidal, Guifre (2015) Fast convergence of imaginary time evolution tensor network algorithms by recycling the environment. Physical Review B - Condensed Matter and Materials Physics, 91 11: 1-15. doi:10.1103/PhysRevB.91.115137
Phase diagram of the J(1)-J(2) Heisenberg model on the kagome lattice
Kolley, F., Depenbrock, S., McCulloch, I. P., Schollwoeck, U. and Alba, V. (2015) Phase diagram of the J(1)-J(2) Heisenberg model on the kagome lattice. Physical Review B, 91 10: 104418-104418. doi:10.1103/PhysRevB.91.104418
Conformal data from finite entanglement scaling
Stojevic, Vid, Haegeman, Jutho, McCulloch I.P., Tagliacozzo, Luca and Verstraete, Frank (2015) Conformal data from finite entanglement scaling. Physical Review B - Condensed Matter and Materials Physics, 91 3: . doi:10.1103/PhysRevB.91.035120
Haldane phase in the hubbard model at 2/3-filling for the organic molecular compound Mo3 S7 (dmit)3
Janani, C., Merino J., McCulloch, I. P. and Powell, B. J. (2014) Haldane phase in the hubbard model at 2/3-filling for the organic molecular compound Mo3 S7 (dmit)3. Physical Review Letters, 113 26: 267204-1-267204-5. doi:10.1103/PhysRevLett.113.267204
Solving nonequilibrium dynamical mean-field theory using matrix product states
Wolf, F. Alexander, McCulloch, Ian P. and Schollwock, Ulrich (2014) Solving nonequilibrium dynamical mean-field theory using matrix product states. Physical Review B - Condensed Matter and Materials Physics, 90 23: . doi:10.1103/PhysRevB.90.235131
Chebyshev matrix product state impurity solver for dynamical mean-field theory
Wolf, F. Alexander, McCulloch, Ian P., Parcollet, Olivier and Schollwoeck, Ulrich (2014) Chebyshev matrix product state impurity solver for dynamical mean-field theory. Physical Review B, 90 11: 115124.1-115124.17. doi:10.1103/PhysRevB.90.115124
Observation of a disordered bosonic insulator from weak to strong interactions
D'Errico, Chiara, Lucioni, Eleonora, Tanzi, Luca, Gori, Lorenzo, Roux, Guillaume, McCulloch, Ian P., Giamarchi, Thierry, Inguscio, Massimo and Modugno, Giovanni (2014) Observation of a disordered bosonic insulator from weak to strong interactions. Physical Review Letters, 113 9: 095301. doi:10.1103/PhysRevLett.113.095301
Zhan, Fei, Sabbatini, Jacopo, Davis, Matthew J. and McCulloch, Ian P. (2014) Miscible-immiscible quantum phase transition in coupled two-component Bose-Einstein condensates in one-dimensional optical lattices. Physical Review A, 90 2: . doi:10.1103/PhysRevA.90.023630
Janani, C., Merino, J., McCulloch, Ian P. and Powell, B. J. (2014) Low-energy effective theories of the two-thirds filled Hubbard model on the triangular necklace lattice. Physical Review B - Condensed Matter and Materials Physics, 90 3: 035120-1-035120-10. doi:10.1103/PhysRevB.90.035120
Piraud, Marie, Cai, Zi, McCulloch, Ian P. and Schollwock, Ulrich (2014) Quantum magnetism of bosons with synthetic gauge fields in one-dimensional optical lattices: A density-matrix renormalization-group study. Physical Review A: Atomic, Molecular, and Optical Physics, 89 6: . doi:10.1103/PhysRevA.89.063618
Domain-wall melting in ultracold-boson systems with hole and spin-flip defects
Halimeh, Jad C., Wollert, Anton, McCulloch, Ian, Schollwock, Ulrich and Barthel, Thomas (2014) Domain-wall melting in ultracold-boson systems with hole and spin-flip defects. Physical Review A - Atomic, Molecular, and Optical Physics, 89 6: . doi:10.1103/PhysRevA.89.063603
Comment on "phase separation in a two-species Bose mixture"
Zhan, Fei and McCulloch, Ian P. (2014) Comment on "phase separation in a two-species Bose mixture". Physical Review A - Atomic, Molecular and Optical Physics, 89 5: . doi:10.1103/PhysRevA.89.057601
Sudden expansion of Mott insulators in one dimension
Vidmar, L., Langer, S., McCulloch, I. P., Schneider, U., Schollwoeck, U. and Heidrich-Meisner, F. (2013) Sudden expansion of Mott insulators in one dimension. Physical Review B, 88 23: 235117.1-235117.16. doi:10.1103/PhysRevB.88.235117
Entanglement spectroscopy of SU(2)-broken phases in two dimensions
Kolley F., Depenbrock S., McCulloch I.P., Schollwock U. and Alba V. (2013) Entanglement spectroscopy of SU(2)-broken phases in two dimensions. Physical Review B - Condensed Matter and Materials Physics, 88 14: 144426.1-144426.9. doi:10.1103/PhysRevB.88.144426
Entanglement entropy scaling of the XXZ chain
Chen, Pochung, Xue, Zhi-long, McCulloch I.P., Chung, Ming-Chiang, Cazalilla, Miguel and Yip S.-K. (2013) Entanglement entropy scaling of the XXZ chain. Journal of Statistical Mechanics: Theory and Experiment, 2013 10: . doi:10.1088/1742-5468/2013/10/P10007
Gangat, A. A., McCulloch, I. P. and Milburn, G. J. (2013) Deterministic many-resonator W entanglement of nearly arbitrary microwave states via attractive Bose-Hubbard simulation. Physical Review X, 3 3: 031009.1-031009.11. doi:10.1103/PhysRevX.3.031009
Dynamical windows for real-time evolution with matrix product states
Phien, Ho N., Vidal, Guifé and McCulloch, Ian P. (2013) Dynamical windows for real-time evolution with matrix product states. Physical Review B, 88 3: 035103.1-035103.9. doi:10.1103/PhysRevB.88.035103
Double zigzag spin chain in a strong magnetic field close to saturation
Shyiko, I. T., McCulloch, I. P., Gumenjuk-Sichevska, J. V. and Kolezhuk, A. K. (2013) Double zigzag spin chain in a strong magnetic field close to saturation. Physical Review B, 88 1: 014403.1-014403.13. doi:10.1103/PhysRevB.88.014403
Expansion dynamics of interacting bosons in homogeneous lattices in one and two dimensions
Ronzheimer, J. P., Schreiber, M., Braun, S., Hodgman, S. S., Langer, S., McCulloch, I. P., Heidrich-Meisner, F., Bloch, I. and Schneider, U. (2013) Expansion dynamics of interacting bosons in homogeneous lattices in one and two dimensions. Physical Review Letters, 110 20: 205301.1-205301.6. doi:10.1103/PhysRevLett.110.205301
Keßler, Stefan, McCulloch, Ian P. and Marquardt, Florian (2013) Creation and dynamics of remote spin-entangled pairs in the expansion of strongly correlated fermions in an optical lattice. New Journal of Physics, 15 053043: 1-24. doi:10.1088/1367-2630/15/5/053043
Infinite boundary conditions for matrix product state calculations
Phien, Ho N., Vidal, Guifre and McCulloch, Ian P. (2012) Infinite boundary conditions for matrix product state calculations. Physical Review B, 86 24: 245107.1-245107.10. doi:10.1103/PhysRevB.86.245107
Fractional excitations in cold atomic gases
Honer, J., Halimeh, J. C., McCulloch, I., Schollwoeck, U. and Buechler, H. P. (2012) Fractional excitations in cold atomic gases. Physical Review a, 86 5: 051606.1-051606.5. doi:10.1103/PhysRevA.86.051606
Bolech, C. J., Heidrich-Meisner, F., Langer, S., McCulloch, I. P., Orso, G. and Rigol, M. (2012) Long-time behavior of the momentum distribution during the sudden expansion of a spin-imbalanced fermi gas in one dimension. Physical Review Letters, 109 11: 110602.1-110602.5. doi:10.1103/PhysRevLett.109.110602
Nature of the spin-liquid ground state of the S=1/2 Heisenberg model on the kagome lattice
Depenbrock, Stefan, McCulloch, Ian P. and Schollwoeck, Ulrich (2012) Nature of the spin-liquid ground state of the S=1/2 Heisenberg model on the kagome lattice. Physical Review Letters, 109 6: . doi:10.1103/PhysRevLett.109.067201
Lanczos algorithm with matrix product states for dynamical correlation functions
Dargel, P.E., Wollert, A., Honecker, A., McCulloch, I.P., Schollwock, U. and Pruschke, T. (2012) Lanczos algorithm with matrix product states for dynamical correlation functions. Physical Review B, 85 20: 205119-1-205119-11. doi:10.1103/PhysRevB.85.205119
Langer, S., Schuetz, M.J.A., McCulloch, I.P., Schollwock, U. and Heidrich-Meisner, F. (2012) Expansion velocity of a one-dimensional, two-component Fermi gas during the sudden expansion in the ballistic regime. Physical Review A, 85 4: 043618-1-043618-7. doi:10.1103/PhysRevA.85.043618
Trotzky, S., Chen, Y. A., Flesch, A., McCulloch, I. P., Schollwock, U., Eisert, J. and Bloch, I. (2012) Probing the relaxation towards equilibrium in an isolated strongly correlated one-dimensional Bose gas. Nature Physics, 8 4: 325-330. doi:10.1038/NPHYS2232
Ground-state properties of antiferromagnetic anisotropic S=1 Heisenberg spin chains
Peters, D., McCulloch, I. P. and Selke, W. (2012) Ground-state properties of antiferromagnetic anisotropic S=1 Heisenberg spin chains. Physical Review B, 85 5 Article No. 054423: . doi:10.1103/PhysRevB.85.054423
Dimerized and trimerized phases for spin-2 bosons in a one-dimensional optical lattice
Chen, Pochung, Xue, Zhi-Long, McCulloch, I. P., Chung, Ming-Chiang and Yip, S.-K. (2012) Dimerized and trimerized phases for spin-2 bosons in a one-dimensional optical lattice. Physical Review A, 85 1: 011601.1-011601.4. doi:10.1103/PhysRevA.85.011601
Stroboscopic observation of quantum many-body dynamics
Kessler, Stefan, Holzner, Andreas, McCulloch, Ian P., von Delft, Jan and Marquardt, Florian (2012) Stroboscopic observation of quantum many-body dynamics. Physical Review A, 85 1 Article No. 011605: . doi:10.1103/PhysRevA.85.011605
Real-time energy dynamics in spin-1/2 Heisenberg chains
Langer, Stephan, Heyl, Markus, McCulloch, Ian P. and Heidrich-Meisner, Fabien (2011) Real-time energy dynamics in spin-1/2 Heisenberg chains. Physical Review B, 84 39 Article No.205115: . doi:10.1103/PhysRevB.84.205115
Statistically induced phase transitions and anyons in 1D optical lattices
Keilmann, Tassilo, Lanzmich, Simon, McCulloch, Ian and Roncaglia, Marco (2011) Statistically induced phase transitions and anyons in 1D optical lattices. Nature Communications, 2 1: 361-1-361-7. doi:10.1038/ncomms1353
Chebyshev matrix product state approach for spectral functions
Holzner, Andreas, Weichselbaum, Arnold, McCulloch, Ian P., Schollwock, Ulrich and von Delft, Jan (2011) Chebyshev matrix product state approach for spectral functions. Physical Review B, 83 19 Article No.195115: . doi:10.1103/PhysRevB.83.195115
Coherent spin-current oscillations in transverse magnetic fields
Steinigeweg, Robin, Langer, Stephan, Heidrich-Meisner, Fabian, McCulloch, Ian P. and Brenig, Wolfram (2011) Coherent spin-current oscillations in transverse magnetic fields. Physical Review Letters, 106 16: . doi:10.1103/PhysRevLett.106.160602
Landau-Zener sweeps and sudden quenches in coupled Bose-Hubbard chains
Kasztelan, C., Trotzky, S., Chen, Y. A.., Bloch, I., McCulloch, I. P., Schollwock, U. and Orso, G. (2011) Landau-Zener sweeps and sudden quenches in coupled Bose-Hubbard chains. Physical Review Letters, 106 15: . doi:10.1103/PhysRevLett.106.155302
Coulomb interaction effects and electron spin relaxation in the one-dimensional Kondo lattice model
Smerat, Sebastian, Schoeller, Herbert, McCulloch, Ian P. and Schollwock, Ulrich (2011) Coulomb interaction effects and electron spin relaxation in the one-dimensional Kondo lattice model. Physical Review B - Condensed Matter and Materials Physics, 83 8: 1-8. doi:10.1103/PhysRevB.83.085111
Quantum criticality in the SO(5) bilinear-biquadratic Heisenberg chain
Alet, F., Capponi, S., Nonne, H., Lecheminant, P. and McCulloch, I. P. (2011) Quantum criticality in the SO(5) bilinear-biquadratic Heisenberg chain. Physical Review B, 83 6: 060407-1-060407-4. doi:10.1103/PhysRevB.83.060407
Boundary quantum critical phenomena with entanglement renormalization
Evenbly, G, Pfeifer, R. N. C., Pico, V., Iblisdir, S., Tagliacozzo, L., McCulloch, I.P. and Vidal, G. (2010) Boundary quantum critical phenomena with entanglement renormalization. Physical Review B - Condensed Matter and Materials Physics, 82 16: 1-4. doi:10.1103/PhysRevB.82.161107
Valence-bond entanglement entropy of frustrated spin chains
Alet, F, McCulloch, IP, Capponi, S and Mambrini, M (2010) Valence-bond entanglement entropy of frustrated spin chains. Physical Review B - Condensed Matter and Materials Physics, 82 9: 1-9. doi:10.1103/PhysRevB.82.094452
Heidrich-Meisner, F., McCulloch, I. P. and Kolezhuk, A. K. (2010) Erratum : Phase diagram of an anisotropic frustrated ferromagnetic spin-1/2 chain in a magnetic field: A density matrix renormalization group study (vol 80, 144417, 2009). Physical Review B, 81 17: 17990-2-17990-2. doi:10.1103/PhysRevB.81.179902
Holzner, Andreas, McCulloch, Ian P., Schollwock, Ulrich, von Delft, Jan and Heidrich-Meisner, Fabian (2009) Kondo screening cloud in the single-impurity Anderson model: A density matrix renormalization group study. Physical Review B, 80 20: 205114-1-205114-8. doi:10.1103/PhysRevB.80.205114
Heidrich-Meisner, F., McCulloch, I. P. and Kolezhuk, A. K. (2009) Phase diagram of an anisotropic frustrated ferromagnetic spin-1/2 chain in a magnetic field: A density matrix renormalization group study. Physical Review B, 80 14: 144417-1-144417-9. doi:10.1103/PhysRevB.80.144417
Langer, S., Heidrich-Meisner, F., Gemmer, J., McCulloch, I. P. and Schollwock, U. (2009) Real-time study of diffusive and ballistic transport in spin-1/2 chains using the adaptive time-dependent density matrix renormalization group method. Physical Review B (Condensed Matter and Materials Physics), 79 21: 214409.1-214409.11. doi:10.1103/PhysRevB.79.214409
Smerat, Sebastian, Schollwock, Ulrich, McCulloch, Ian P. and Schoeller, Herbert (2009) Quasiparticles in the Kondo lattice model at partial fillings of the conduction band using the density matrix renormalization group. Physical Review B, 79 23: 23107-1-23107-9. doi:10.1103/PhysRevB.79.235107
Smerat, S, Schollwock, U, McCulloch, IP and Schoeller, H (2009) Quasiparticles in the Kondo lattice model at partial fillings of the conduction band using the density matrix renormalization group (vol 79, 235107, 2009). Physical Review B, 79 24: . doi:10.1103/PhysRevB.79.249902
Barthel, T., Kasztelan, C., McCulloch, I. P. and Schollwock, U. (2009) Magnetism, coherent many-particle dynamics, and relaxation with ultracold bosons in optical superlattices. Physical Review A (Atomic, Molecular and Optical Physics), 79 5: 053627-1-053627-19. doi:10.1103/PhysRevA.79.053627
Spin-one Heisenberg antiferromagnetic chain with exchange and single-ion anisotropies
Peters, D., McCulloch, I. P. and Selke, W. (2009) Spin-one Heisenberg antiferromagnetic chain with exchange and single-ion anisotropies. Physical Review B, 79 13: 132406-1-132406-4. doi:10.1103/PhysRevB.79.132406
Field-controlled spin current in frustrated spin chains
Kolezhuk, A. K. and McCulloch, I. P. (2009) Field-controlled spin current in frustrated spin chains. Condensed Matter Physics, 12 3: 429-434. doi:10.5488/CMP.12.3.429
Classical and quantum anisotropic Heisenberg antiferromagnets
Selke, W., Bannasch, G., Holtschneider, M., McCulloch, I. P., Peters, D. and Wessel, S. (2009) Classical and quantum anisotropic Heisenberg antiferromagnets. Condensed Matter Physics, 12 4: 547-558. doi:10.5488/CMP.12.4.547
Probing local relaxation of cold atoms in optical superlattices
Flesch, A., Cramer, M., McCulloch, I. P., Schollwock, U. and Eisert, J. (2008) Probing local relaxation of cold atoms in optical superlattices. Physical Review A, 78 3: . doi:10.1103/PhysRevA.78.033608
Quasiperiodic Bose-Hubbard model and localization in one-dimensional cold atomic gases
Roux, G., Barthel, T., McCulloch, I. P., Kollath, C., Schollwock, U. and Giamarchi, T. (2008) Quasiperiodic Bose-Hubbard model and localization in one-dimensional cold atomic gases. Physical Review A, 78 2: . doi:10.1103/PhysRevA.78.023628
Exploring local quantum many-body relaxation by atoms in optical superlattices
Cramer, M., Flesch, A., McCulloch, I. P., Schollwock, U. and Eisert, J. (2008) Exploring local quantum many-body relaxation by atoms in optical superlattices. Physical Review Letters, 101 6: Article Number: 063001. doi:10.1103/PhysRevLett.101.063001
Excitations in two-component Bose gases
Kleine, A., Kollath, C., McCulloch, I. P., Giamarchi, T. and Schollwock, U. (2008) Excitations in two-component Bose gases. New Journal of Physics, 10 . doi:10.1088/1367-2630/10/4/045025
Vector chiral order in frustrated spin chains
McCulloch, I. P., Kube, R., Kurz, M., Kleine, A., Schollwock, U. and Kolezhuk, A. K. (2008) Vector chiral order in frustrated spin chains. Physical Review B: Condensed Matter and Materials Physics, 77 9: 094404-1-094404-7. doi:10.1103/PhysRevB.77.094404
Corboz, P., Troyer, M, Kleine, A., McCulloch, I. P., Schollwock, U. and Assaad, F. F. (2008) Systematic errors in Gaussian quantum Monte Carlo and a systematic study of the symmetry projection method. Physical Review B, 77 8 Article # 085108: . doi:10.1103/PhysRevB.77.085108
Spin-charge separation in two-component Bose gases
Kleine, A., Kollath, C., McCulloch, I. P., Giamarchi, T. and Schollwock, U. (2008) Spin-charge separation in two-component Bose gases. Physical Review A, 77 1: 13607-1-13607-6. doi:10.1103/PhysRevA.77.013607
From density-matrix renormalization group to matrix product states
McCulloch, Ian P. (2007) From density-matrix renormalization group to matrix product states. Journal of Statistical Mechanics: Theory and Experiment, 27 4: P10014-1-P10014-19. doi:10.1088/1742-5468/2007/10/P10014
Friedrich, A., Kolezhuk, A. K., McCulloch, I. P. and Schollwock, U. (2007) Edge singularities in high-energy spectra of gapped one-dimensional magnets in strong magnetic fields. Physical Review B, 75 9 Article # 094414: . doi:10.1103/PhysRevB.75.094414
Spinful bosons in an optical lattice
Bergkvist, Sara, McCulloch, Ian P. and Rosengren, Anders (2006) Spinful bosons in an optical lattice. Physical Review A, 74 5 Article # 053419: . doi:10.1103/PhysRevA.74.053419
Modulation spectroscopy with ultracold fermions in an optical lattice
Kollath, C., Iucci, A., McCulloch, I. P. and Giamarchi, T. (2006) Modulation spectroscopy with ultracold fermions in an optical lattice. Physical Review a, 74 4 Article # 041604: . doi:10.1103/PhysRevA.74.041604
The ALPS Project: Open Source Software for Strongly Correlated Systems
Alet, F., Dayal, P., Grzesik, A., Honecker, A., Koerner, M., Laeuchli, A., Manmana, S. R., McCulloch, I. P., Michel, F., Noack, R. M., Schmid, G., Schollwoeck, U., Stoeckli, F., Todo, S., Trebst, S., Troyer, M., Werner, P. and Wessel, S. (2005) The ALPS Project: Open Source Software for Strongly Correlated Systems. Journal of the Physical Society of Japan, 74 30-35. doi:10.1143/JPSJS.74S.30
Geometry and the hidden order of Luttinger liquids: the universality of squeezed space
Kruis, H. V., McCulloch, I. P., Nussinov, Z. and Zaanen, J. (2004) Geometry and the hidden order of Luttinger liquids: the universality of squeezed space. Physical Review B, 70 7: 075109.1-075109.21. doi:10.1103/PhysRevB.70.075109
NMR evidence for a two-step phase separation in Nd1.85Ce0.15CuO4-delta
Bakharev, ON, Abu-Shiekah, IM, Brom, HB, Nugroho, AA, McCulloch, IP and Zaanen, J (2004) NMR evidence for a two-step phase separation in Nd1.85Ce0.15CuO4-delta. Physical Review Letters, 93 3: 037002-1. doi:10.1103/PhysRevLett.93.037002
Magnetism in the dilute Kondo lattice model
Gulacsi, M, McCulloch, IP, Juozapavicius, A and Rosengren, A (2004) Magnetism in the dilute Kondo lattice model. Physical Review B, 69 17: . doi:10.1103/PhysRevB.69.174425
Geometry and topological order in the Luttinger liquid state
Kruis, H. V., McCulloch, I. P., Nussinov, Z. and Zaanen, J. (2004) Geometry and topological order in the Luttinger liquid state. Europhysics Letters, 65 4: 512-518. doi:10.1209/i2003-10114-3
McCulloch, I. P. and Gulacsi, M (2003) Comment on "Equivalence of the variational matrix product method and the density matrix renormalization group applied to spin chains" by J. Dukelsky et al.. Europhysics Letters, 61 1: 138-139. doi:10.1209/epl/i2003-00266-0
Ferromagnetic phases in the Kondo lattice model
Juozapavicius, A, McCulloch, IP, Gulacsi, M and Rosengren, A (2002) Ferromagnetic phases in the Kondo lattice model. Philosophical Magazine B-Physics of Condensed Matter Statistical Mechanics Electronic Optical and Magnetic Properties, 82 11: 1211-1224. doi:10.1080/13642810210131809
The non-Abelian density matrix renormalization group algorithm
McCulloch, I. P. and Gulacsi, M. (2002) The non-Abelian density matrix renormalization group algorithm. Europhysics Letters, 57 6: 852-858. doi:10.1209/epl/i2002-00393-0
Localized spin ordering in Kondo lattice models
McCulloch, IP, Juozapavicius, A, Rosengren, A and Gulacsi, M (2002) Localized spin ordering in Kondo lattice models. Physical Review B, 65 5: . doi:10.1103/PhysRevB.65.052410
Ferromagnetism in Kondo lattice models
McCulloch, IP, Juozapavicius, A, Rosengren, A and Gulacsi, M (2001) Ferromagnetism in Kondo lattice models. Philosophical Magazine Letters, 81 12: 869-875. doi:10.1080/09500830110092390
Total spin in the density matrix renormalization group algorithm
McCulloch, IP and Gulacsi, M (2001) Total spin in the density matrix renormalization group algorithm. Philosophical Magazine Letters, 81 6: 447-453. doi:10.1080/09500830110040009
Two-dimensional Hubbard model close to half-filling
McCulloch, IP and Gulacsi, M (1997) Two-dimensional Hubbard model close to half-filling. Philosophical Magazine B-Physics of Condensed Matter Statistical Mechanics Electronic Optical and Magnetic Properties, 76 5: 819-825. doi:10.1080/01418639708241145
Expansion after a geometric quench of an atomic polarized attractive Fermi gas in one dimension
Bolech, C. J., Heidrich-Meisner, F., Langer, S., McCulloch, I. P., Orso, G. and Rigol, M. (2013). Expansion after a geometric quench of an atomic polarized attractive Fermi gas in one dimension. In: 21st International Laser Physics Workshop. 21st International Laser Physics Workshop, Calgary Canada, (2-9). Jul 23-27, 2012. doi:10.1088/1742-6596/414/1/012033
Quantum Heisenberg antiferromagnetic chains with exchange and single-ion anisotropies
Peters, D., McCulloch, I. P. and Selke, W. (2010). Quantum Heisenberg antiferromagnetic chains with exchange and single-ion anisotropies. In: Goll, G, Lohneysen, HV, Loidl, A, Pruschke, T, Richter, M, Schultz, L, Surgers, C and Wosnitza, J, International Conference on Magnetism, ICM 2009. International Conference on Magnetism (ICM 2009), Karlsruhe, Germany, (1-4). 26-31 July 2009. doi:10.1088/1742-6596/200/2/022046
Classical and quantum anisotropic Heisenberg antiferromagnets
Selke, W., Bannasch, G., Holtschneider, M., McCulloch, I. P. and Peters, D. (2009). Classical and quantum anisotropic Heisenberg antiferromagnets. In: W. Ebeling, I. Mryglod, N. Plakida and A. Zagorodny, Statistical Physics: Modern Trends and Applications. Invited papers and selected Proceedings of the 3rd Conference on Statistical Physics. StatPhys2009. 3rd Conference on Statistical Physics: Modern Trends and Applications, Lviv, Ukraine, (547-558). 23-25 June, 2009. doi:10.5488/CMP.12.4.547
Simulating Bose gases with tensor product states
Ferris, Andy, Davis, Matthew and McCulloch, Ian (2009). Simulating Bose gases with tensor product states. In: ACOLS ACOFT. ACOLS ACOFT 09, The University of Adelaide, (266-267). 29/11/09 - 3/12/09.
The ALPS project release 1.3: Open-source software for strongly correlated systems
Albuquerque, A. F., Alet, F., Corboz, P., Dayal, P., Feiguin, A., Fuchs, S., Gamper, L., Gull, E., Gurtler, S., Honecker, A., Igarashi, R., Korner, M., Kozhevnikov, A., Lauchli, A., Manmana, S. R., Matsumoto, M., McCulloch, I. P., Michel, F., Noack, R. M., Pawlowski, G., Pollet, L., Pruschke, T., Schollwock, U., Todo, S., Trebst, S., Troyer, M., Werner, P., Wessel, S. and ALPS Collaboration (2007). The ALPS project release 1.3: Open-source software for strongly correlated systems. In: H. Harima, H. Kawamura, Y. Kitaoka, H. Kohno, K. Miyake, Y. Suzuki, H. Sakakima and G.-q. Zheng, Proceedings of the 17th International Conference on Magnetism. 17th International Conference on Magnetism (ICM 2006), Kyoto, Japan, (1187-1193). 20-25 August 2006. doi:10.1016/j.jmmm.2006.10.304
Density matrix renormalization group algorithm and the two-dimensional t-J model
McCulloch, IP, Bishop, AR and Gulacsi, M (2001). Density matrix renormalization group algorithm and the two-dimensional t-J model. In: Philosophical Magazine B-Physics of Condensed Matter Statistical Mechanics Electronic Optical and Magnetic Properties. 2nd International Summer School on Strongly Correlated Systems, Debrecen Hungary, (1603-1613). Sep 04-09, 2000. doi:10.1080/13642810108208574
Density matrix renormalisation group method and symmetries of the Hamiltonian
McCulloch, IP and Gulacsi, M (2000). Density matrix renormalisation group method and symmetries of the Hamiltonian. In: Australian Journal of Physics. 9th Gordon Godfrey Workshop on Condensed Matter Physics, Sydney Australia, (597-612). Nov 08, 1999.
Phase diagram of the 1D Kondo lattice model
McCulloch, IP, Gulacsi, M, Caprara, S, Jazavaou, A and Rosengren, A (1999). Phase diagram of the 1D Kondo lattice model. In: Journal of Low Temperature Physics. International Conference on Physics and Chemistry of Molecular and Oxide Superconductors (MOS-99), Stockholm Sweden, (323-328). Jul 28-Aug 02, 1999. doi:10.1023/A:1022557314114
Strong coupling regime in the two-dimensional Hubbard model
McCulloch, IP and Gulacsi, M (1998). Strong coupling regime in the two-dimensional Hubbard model. In: Journal of Magnetism and Magnetic Materials. ICM 97 Meeting, Cairns Australia, (316-318). 1997. doi:10.1016/S0304-8853(98)00018-3
Classical and quantum anisotropic Heisenberg antiferrogmagnets
Classical and quantum anisotropic Heisenberg antiferrogmagnets (2009) . Edited by Ihor Tukhnovskii. The 3rd conference on statistical physics dedicated to the 100th anniversary of Mykola Bogolyubov, 23-25 June 2009, Lviv, Ukraine.
Quantum thermodynamics of ultra-cold atoms
(2019–2021) ARC Discovery Projects
Simulating quantum states of matter: connecting theory to applications in science and technology.
(2015–2019) ARC Future Fellowships
Advanced Superfluid Physics Facility
(2015–2016) UQ Major Equipment and Infrastructure
ARC Centre of Excellence for Engineered Quantum Systems (EQuS)
(2011–2017) ARC Centres of Excellence
(2010–2012) ARC Discovery Projects
Many body localization and topological states in two dimensional quantum matter
Doctor Philosophy — Principal Advisor
Other advisors:
Frustrated spin systems, an MPS approach
(2017) Doctor Philosophy — Principal Advisor
Other advisors:
Simulation of Stochastic Transport in Complex Systems Using Quantum Techniques
(2014) Master Philosophy — Principal Advisor
Other advisors:
Tensor network approaches: Ground states and dynamics in quantum many-body systems
(2014) Doctor Philosophy — Principal Advisor
Mo3S7(dmit)3: From material to models
(2015) Doctor Philosophy — Joint Principal Advisor
Other advisors:
Simulation of Anyons Using Symmetric Tensor Network Algorithms
(2011) Doctor Philosophy — Associate Advisor
Note for students: The possible research projects listed on this page may not be comprehensive or up to date. Always feel free to contact the staff for more information, and also with your own research ideas.
Tensor Network / Matrix Product State methods for computational quantum many-body problems
Tensor Networks provide a representation of a quantum many-body wave-function (or a classical partition function) that is suitable for computational methods, mainly for low-dimensional problems (1D and 2D). The most mature branch of tensor networks is known as Matrix Product States (MPS), often called DMRG. These days this is the widely used method to solve 1-dimensional quantum many-body problems. At UQ, we have developed the Matrix Product Toolkit, which is a comprehensive software toolkit for many kinds of MPS-based computations, including ground-states, real-time dynamics, and thermal and dissipative states. This software toolbox has been used in approximately 70 research publications in various fields of condensed matter and quantum science, ranging from ultra-cold atoms in optical lattices, ion traps, Josephson Junction arrays, strongly correlated systems, frustrated magnetism, topological order, dynamical mean-field theory. See my publications at ResearcherID for more details.
I am happy to talk to you to find a suitable project at any level, from summer project to PhD. Possible short projects would be, for example, learning about the Matrix Product Toolkit and trying some calculations (depending on the details and rate of progress this could lead to a research publication), or implementing a simple MPS or tensor network algorithm in Python or Matlab.
Possible PhD projects would be based around one of three possible themes: