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Claudius Hubig

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.

Contact Details

Max-Planck-Institut für Quantenoptik
Hans-Kopfermann-Str. 1
85748 Garching
arXiv author page · at MPQ
Formerly: at the Schollwöck Chair · at ExQM

Research Interests

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.


  1. 1901.05824: Sebastian Paeckel, Thomas Köhler, Andreas Swoboda, Salvatore R. Manmana, Ulrich Schollwöck and Claudius Hubig: Time-evolution methods for matrix-product states
  2. 1812.03801: Claudius Hubig and J. Ignacio Cirac: Time-dependent study of disordered models with infinite projected entangled pair states
  3. 1811.07178: Mattia Mena, Nora Hänni, Simon Ward, Eva Hirtenlechner, Robert Bewley, Claudius Hubig, Ulrich Schollwöck, Bruce Normand, Karl W. Krämer, Des F. McMorrow and Christian Rüegg: Thermal control of spin excitations in the coupled Ising-chain material RbCoCl3
  4. 1811.00048: Teresa E. Reinhard, Uliana Mordovina, Claudius Hubig, Joshua S. Kretchmer, Ulrich Schollwöck, Heiko Appel, Michael A. Sentef and Angel Rubio: Density-matrix embedding theory study of the one-dimensional Hubbard-Holstein model
  5. 1810.09799: Imre Hagymási, Claudius Hubig and Ulrich Schollwöck: Interaction quench and thermalization in a one-dimensional topological Kondo insulator
  6. 1808.10804 [SciPost]: Claudius Hubig: Abelian and non-abelian symmetries in infinite projected entangled pair states
  7. 1711.01104 [PRB]: Claudius Hubig, Jutho Haegeman and Ulrich Schollwöck: Error estimates for extrapolations with matrix-product states
  8. 1710.04847 [PNAS]: Ilia Khait, Patrick Azaria, Claudius Hubig, Ulrich Schollwöck and Assa Auerbach: Doped Kondo chain, a heavy Luttinger liquid
  9. 1705.01259 [PRB]: Anup K. Bera, Bella Lake, Fabian H. L. Essler, Laurens Vanderstraeten, Claudius Hubig, Ulrich Schollwöck, A. T. M. Nazmul Islam, Astrid Schneidewind and Diana L. Quintero-Castro: Spinon confinement in a quasi one dimensional anisotropic Heisenberg magnet
  10. 1611.02498 [PRB]: Claudius Hubig, Ian P. McCulloch and Ulrich Schollwöck: Generic construction of efficient matrix product operators
  11. 1609.08518 [PRB]: Zi Cai, Claudius Hubig and Ulrich Schollwöck: Universal long-time behavior of stochastically driven interacting quantum systems
  12. 1501.05504 [PRB] : Claudius Hubig, Ian P. McCulloch, Ulrich Schollwöck and F. Alexander Wolf: Strictly single-site DMRG algorithm with subspace expansion


  1. 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
  2. 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



Workshops Co-organised

Teaching Experience

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)



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.