Postdoc in the group of Ignacio Cirac at the Max Planck Institute of Quantum Optics in Garching, working on the development, implementation and application of tensor network algorithms.
Research is focused on numerical and algorithmic improvements to tensor network methods in condensed matter physics such as the DMRG, time evolution algorithms on MPS and generalisations of these methods to non-one-dimensional networks. Of particular interest is also further interlinking with the numerical linear algebra community as well as the application of DMRG in novel contexts as inner solvers of other methods (such as DMFT or DMET).
Work on the tensor network toolkit SyTen has been ongoing since 2015. SyTen is capable of handling arbitrary-rank tensors with nonabelian symmetries such as SU(2)-Spin and provides a high degree of parallelisation.
For one-dimensional systems, ground-state search with MPS-DMRG (single-site and two-site), various time evolution methods (Krylov, Taylor, TEBD, TDVP and the MPO method) and associated tooling for MPS and MPO generation and arithmetic are implemented. Some basic support (DMRG, Krylov time evolution etc.) for binary tree tensor networks and MPS with a local basis optimisation also exists.
A relatively recent addition is a set of Python bindings which allow for a very fast and flexible definition of new physical systems in a few lines of interpreted, not compiled, code. Additionally, by also exposing the entire tensor network library, it becomes possible to quickly develop and implement new tensor algorithms.
Most recently, work on an implementation of infinite projected entangled pair states for two-dimensional systems was merged into the master branch. By using the basic tensor library, this implementation can make use of arbitrary symmetries leading to a great speed-up compared to an ‘unsymmetric’ calculation. While this IPEPS implementation currently uses swap-gates to handle fermionic systems, a second implementation which is on the way uses a smarter, fermionic tensor class.
This newer smart tensor class offers automatic contraction of matching legs and handling of fermionic permutation rules. Under the hood, it relies on the original tensor class to provide high performance tensor operations. It is expected that it can be used in the future to make both even better use of the Python bindings and accelerate the implementation of new algorithms.
- arXiv:1808.10804: Claudius Hubig: Abelian and non-abelian symmetries in infinite projected entangled pair states
- Phys. Rev. B 97, 045125 [arXiv]: Claudius Hubig, Jutho Haegeman, Ulrich Schollwöck: Error estimates for extrapolations with matrix-product states
- PNAS 2018, 201719374 [arXiv]: Ilia Khait, Patrick Azaria, Claudius Hubig, Ulrich Schollwöck, Assa Auerbach: Doped Kondo chain, a heavy Luttinger liquid
- Phys. Rev. B 96, 054423 [arXiv]: Anup K. Bera, Bella Lake, Fabian H. L. Essler, Laurens Vanderstraeten, Claudius Hubig, Ulrich Schollwöck, A. T. M. Nazmul Islam, Astrid Schneidewind, Diana L. Quintero-Castro: Spinon confinement in a quasi one dimensional anisotropic Heisenberg magnet
- Phys. Rev. B 95, 035129 [arXiv]: Claudius Hubig, Ian P. McCulloch and Ulrich Schollwöck: Generic construction of efficient matrix product operators
- Phys. Rev. B 96, 054303 [arXiv]: Zi Cai, Claudius Hubig and Ulrich Schollwöck: Universal long-time behavior of stochastically driven interacting quantum systems
- Phys. Rev. B 91, 155115 [arXiv]: Claudius Hubig, Ian P. McCulloch, Ulrich Schollwöck and F. Alexander Wolf: Strictly single-site DMRG algorithm with subspace expansion
- PhD Thesis [at LMU]: Symmetry-Protected Tensor Networks; submitted to the Faculty of Physics at LMU Munich on 2017-08-31, defended on 2017-10-30, refereed by Ulrich Schollwöck and Norbert Schuch
- BSc Thesis: Spin Dynamics in Adiabatic Transport through Quantum Dots; submitted to the Faculty of Physics at TU Berlin on 2012-07-03, supervised by Anja Metelmann, refereed by Tobias Brandes and Andreas Knorr
- 11/2018 (upcoming): Tensor Network based approaches to Quantum Many-Body Systems, Dresden: Symmetries in Tensor Networks
- 11/2018 (upcoming): Arnold Sommerfeld Center, Munich: PhD Prize Colloquium: Evolving Tensor Networks
- 07/2018: Seminar of the Institute for Theoretical Physics, Göttingen: Applications of Tensor Networks in Ab Initio Methods
- 06/2018: Optimising, Renormalising, Evolving and Quantising Tensor Networks, Dresden: Symmetry implementations in tensor networks
- 03/2018: Frühjahrstagung der DPG, Berlin: Error estimates for extrapolations with matrix-product states
- 02/2018: Entanglement in Strongly Correlated Systems, Benasque: Error estimates for extrapolations with matrix-product states [slides] [local copy]
- 11/2017: 2017 School, European Tensor Network, Ghent: Tutorial on DMRG with Subspace Expansion; Python script
- 09/2017: Arnold Sommerfeld School on Numerical Methods for Strongly Correlated Many-Body Systems, Munich: Tutorial & Hands-On Session on DMRG and MPS Methods
- 04/2017: Theory Department, Max-Planck-Institut für Struktur und Dynamik, Hamburg: Time Evolution with Matrix-Product States
- 03/2017: Theory Seminar, Max-Planck-Institut für Quantenoptik, Garching: DMRG with Subspace Expansion on Symmetry-Protected Tensor Networks
- 03/2017: Frühjahrstagung der DPG, Dresden: Generic Construction of Efficient Matrix Product Operators
- 01/2017: Theory Winter School, MagLab, Tallahassee: Tutorial & Hands-On Session on DMRG and DMRG+DMFT
- 03/2016: Frühjahrstagung der DPG, Regensburg: DMRG on Binary Tree Tensor Networks
- 01/2016: Fritz Haber Institut der Max-Planck-Gesellschaft, Berlin: Symmetries in Tensor Networks and Subspace Expansion with DMRG
- 09/2017: Tensor Computation Workshop, Flatiron Institute, New York City: Claudius Hubig and Ulrich Schollwöck: Error Estimates for Matrix-Product States
- 09/2017: Arnold Sommerfeld School on Numerical Methods for Strongly Correlated Many-Body Systems, Munich: Claudius Hubig and Ulrich Schollwöck: Error Estimates for Matrix-Product States
- 05/2017: Munich Quantum Center Workshop: Andreas Swoboda, Nils-Oliver Linden, Ulrich Schollwöck and Claudius Hubig: Time Evolution for Matrix-Product States with the Krylov Subspace Method
- 10/2016: Munich Quantum Symposium: Claudius Hubig, Ian P. McCulloch and Ulrich Schollwöck: A Generic Algorithm for the Construction of Efficient Matrix Product Operators
- 06/2016: International Summer School on Computational Quantum Materials, Sherbrooke: Claudius Hubig, Ian P. McCulloch and Ulrich Schollwöck: Generic Algorithm for the Construction of Efficient Matrix Product Operators
- 02/2016: Entanglement in Strongly Correlated Systems, Benasque: Claudius Hubig and Ulrich Schollwöck: DMRG on Binary Tree Tensor Networks
- 11/2015: WEH-Workshop Isolated Quantum Many-Body Systems out of Equilibrium, Bad Honnef: Claudius Hubig, Fabian H. L. Essler and Ulrich Schollwöck: Spin Excitations in a Staggered Magnetic Field
- 02/2015: Advanced Computational Methods for Strongly Correlated Quantum Systems, Würzburg: Claudius Hubig, Ian P. McCulloch, Ulrich Schollwöck and F. Alexander Wolf: A Strictly Single-Site DMRG Algorithm with Subspace Expansion
- 09/2014: Munich Quantum Day: Claudius Hubig, F. Alexander Wolf and Ulrich Schollwöck: Algorithmic Advancements in DMRG
- Summer 2017
- Supervision of Bachelor thesis project: Study of a Sampling Method for Singular Values
- Summer 2016
- Tutoring for Numerische Mathematik (BSc, LMU)
- Summer 2016
- Supervision of Bachelor thesis project: Parallelized Time Evolution on the Heisenberg Spin Chain with Matrix Product States
- Summer 2015
- Tutoring for Advanced Statistical Physics (MSc, LMU)
- Winter 2014/15
- Tutoring for Thermodynamik und Statistische Physik (BSc, LMU)
- Summer 2014
- Tutoring for Advanced Statistical Physics (MSc, LMU)
- Arnold Sommerfeld PhD Prize, 2017
Arnold Sommerfeld Center, LMU Munich
- Deutschlandstipendium, 2011/2012
TU Berlin & Robert Bosch GmbH
- since 11/2017
- Postdoc in the group of Ignacio Cirac, Max Planck Institute of Quantum Optics, Garching, Germany.
- 10/2013 - 10/2017
- PhD Student at the Chair of Uli Schollwöck, LMU Munich, Germany. Funded by the ExQM Graduate School and the Nanosystems Initiative Munich. Title of thesis: Symmetry-Protected Tensor Networks.
- 09/2012 - 07/2013
- Read Applied Mathematics (Part III) at Hughes Hall, University of Cambridge, United Kingdom. Graduated with Masters of Advanced Studies in Applied Mathematics.
- 10/2009 - 07/2012
- Read Physics at TU Berlin. Graduated with Bachelor of Science in Physics, title of thesis: Spin Dynamics in Adiabatic Transport through Quantum Dots. Partially funded by Deutschlandstipendium in 2011/2012.