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Associate Professor Ian McCulloch

Associate Professor

School of Mathematics and Physics
Faculty of Science
ianmcc@physics.uq.edu.au
+61 7 336 52473

Overview

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.

Research Interests

  • Matrix Product Toolkit
    Dr McCulloch is the primary author of the Matrix Product Toolkit of computational tools for modelling many-body quantum systems. The toolkit includes algorithms for finding groundstates, excited states, real-time evolution and spectral methods, thermal states, higher moments of expectation values, and includes easy-to-use methods for constructing matrix product operator representations of arbitrary observables. The website for the Matrix Product Toolkit is https://people.smp.uq.edu.au/IanMcCulloch/mptoolkit
  • Computational methods / Tensor Networks / DMRG / MPS
    Tensor Networks provide a theoretical framework that captures the important properties of quantum systems (such as entanglement) in a way that also allows use of algebraic properties such as geometric and internal symmetries. The result is a framework for computational methods that combines powerful algebraic methods with efficient numerical techniques that can make good use of modern computational architectures (such as GPU devices) to give tools for modelling many-body quantum systems at a microscopic level. These tools have many applications, from fundamental physics such as the classification of topological states of matter, to applications in real materials and devices, such as ultra-cold atomic gases, and quantum-engineered devices.
  • Topological materials
    MPS methods are a key tool for the characterization and simulation of topological states of matter, bridging the gulf between 'toy' models that are exactly solvable, versus real materials that have complicated interactions and cannot be solved analytically. Analysing the properties of candidate models that exhibit topological order is a key area where computational methods are having a big impact, bridging this gulf between theoretical models and experimentally realizable materials. A specific example is models of frustrated magnetism, which have been shown using computational methods to realize exotic topological phases that have otherwise only been predicted in simplified (and unphysical) toy models.
  • Non-equilibrium dynamics and thermalization
    While the statistical mechanics of the thermal equilibrium state has been well understood for many years now, a key question is how thermal states arise at the level of microscopic dynamics. Computational methods are a key tool to uncover the mechanisms of thermalisation at the quantum level.
  • Quantum simulators
    The idea behind quantum simulation is to produce a device that is hard-coded to solving some specific problem that is difficult to solve on a classical computer. Computational methods play a key role in the development of quantum simulation, to validate experimental apparatus, and to provide a framework for classical computation that a truly quantum device should be able to surpass. If we can simulate it using a classical computer, your device isn't really "quantum"!

Research Impacts

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.

Qualifications

  • Doctor of Philosophy, Australian National University

Publications

View all Publications

Grants

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Supervision

View all Supervision

Available Projects

  • 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:

    • Continued development of the Matrix Product Toolkit (new algorithms, or optimizing existing algorithms). The toolkit is written in C++, so experience in modern C++ highly desirable.
    • Development of new Tensor Network algorithms outside the current scope of the Toolkit, eg PEPS, MERA, ... Good computational skills required, not necessarily in C++.
    • Applications of the Toolkit to any relevant area, either continuing existing research streams or new applications (aside from the above, there are possible applications in neural networks and deep learning, compression algorithms, quantum chemistry, nuclear physics, lattice gauge theory).

View all Available Projects

Publications

Journal Article

Conference Publication

  • 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

Edited Outputs

Grants (Administered at UQ)

PhD and MPhil Supervision

Current Supervision

  • Matrix Product State Study of Strongly-interacting Systems and Quantum Phase Transitions

    Doctor Philosophy — Principal Advisor

    Other advisors:

Completed Supervision

Possible Research Projects

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:

    • Continued development of the Matrix Product Toolkit (new algorithms, or optimizing existing algorithms). The toolkit is written in C++, so experience in modern C++ highly desirable.
    • Development of new Tensor Network algorithms outside the current scope of the Toolkit, eg PEPS, MERA, ... Good computational skills required, not necessarily in C++.
    • Applications of the Toolkit to any relevant area, either continuing existing research streams or new applications (aside from the above, there are possible applications in neural networks and deep learning, compression algorithms, quantum chemistry, nuclear physics, lattice gauge theory).

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ResearcherID: A-6037-2011

ORCID: 0000-0002-8983-6327

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