Papers · Theses · Talks · Posters · Workshops · Teaching · Awards · CV
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
MaxPlanckInstitut für Quantenoptik
HansKopfermannStr. 1
85748 Garching
claudius.hubig@mpq.mpg.de
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 nononedimensional 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 arbitraryrank tensors with nonabelian symmetries such as SU(2)Spin and provides a high degree of parallelisation.
For onedimensional systems, groundstate search with MPSDMRG (singlesite and twosite), 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 twodimensional 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 speedup compared to an ‘unsymmetric’ calculation. While this IPEPS implementation currently uses swapgates 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.
Papers
 1901.05824: Sebastian Paeckel, Thomas Köhler, Andreas Swoboda, Salvatore R. Manmana, Ulrich Schollwöck and Claudius Hubig: Timeevolution methods for matrixproduct states
 1812.03801: Claudius Hubig and J. Ignacio Cirac: Timedependent study of disordered models with infinite projected entangled pair states
 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 Isingchain material RbCoCl3
 1811.00048: Teresa E. Reinhard, Uliana Mordovina, Claudius Hubig, Joshua S. Kretchmer, Ulrich Schollwöck, Heiko Appel, Michael A. Sentef and Angel Rubio: Densitymatrix embedding theory study of the onedimensional HubbardHolstein model
 1810.09799: Imre Hagymási, Claudius Hubig and Ulrich Schollwöck: Interaction quench and thermalization in a onedimensional topological Kondo insulator
 1808.10804 [SciPost]: Claudius Hubig: Abelian and nonabelian symmetries in infinite projected entangled pair states
 1711.01104 [PRB]: Claudius Hubig, Jutho Haegeman and Ulrich Schollwöck: Error estimates for extrapolations with matrixproduct states
 1710.04847 [PNAS]: Ilia Khait, Patrick Azaria, Claudius Hubig, Ulrich Schollwöck and Assa Auerbach: Doped Kondo chain, a heavy Luttinger liquid
 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. QuinteroCastro: Spinon confinement in a quasi one dimensional anisotropic Heisenberg magnet
 1611.02498 [PRB]: Claudius Hubig, Ian P. McCulloch and Ulrich Schollwöck: Generic construction of efficient matrix product operators
 1609.08518 [PRB]: Zi Cai, Claudius Hubig and Ulrich Schollwöck: Universal longtime behavior of stochastically driven interacting quantum systems
 1501.05504 [PRB] : Claudius Hubig, Ian P. McCulloch, Ulrich Schollwöck and F. Alexander Wolf: Strictly singlesite DMRG algorithm with subspace expansion
Theses
 PhD Thesis [at LMU]: SymmetryProtected Tensor Networks; submitted to the Faculty of Physics at LMU Munich on 20170831, defended on 20171030, 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 20120703, supervised by Anja Metelmann, refereed by Tobias Brandes and Andreas Knorr
Talks
 11/2018: Tensor Network based approaches to Quantum ManyBody Systems, Dresden: Symmetries in Tensor Networks [slides]
 11/2018: 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 matrixproduct states
 02/2018: Entanglement in Strongly Correlated Systems, Benasque: Error estimates for extrapolations with matrixproduct 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 ManyBody Systems, Munich: Tutorial & HandsOn Session on DMRG and MPS Methods
 04/2017: Theory Department, MaxPlanckInstitut für Struktur und Dynamik, Hamburg: Time Evolution with MatrixProduct States
 03/2017: Theory Seminar, MaxPlanckInstitut für Quantenoptik, Garching: DMRG with Subspace Expansion on SymmetryProtected Tensor Networks
 03/2017: Frühjahrstagung der DPG, Dresden: Generic Construction of Efficient Matrix Product Operators
 01/2017: Theory Winter School, MagLab, Tallahassee: Tutorial & HandsOn Session on DMRG and DMRG+DMFT
 03/2016: Frühjahrstagung der DPG, Regensburg: DMRG on Binary Tree Tensor Networks
 01/2016: Fritz Haber Institut der MaxPlanckGesellschaft, Berlin: Symmetries in Tensor Networks and Subspace Expansion with DMRG
Posters
 09/2017: Tensor Computation Workshop, Flatiron Institute, New York City: Claudius Hubig and Ulrich Schollwöck: Error Estimates for MatrixProduct States
 09/2017: Arnold Sommerfeld School on Numerical Methods for Strongly Correlated ManyBody Systems, Munich: Claudius Hubig and Ulrich Schollwöck: Error Estimates for MatrixProduct States
 05/2017: Munich Quantum Center Workshop: Andreas Swoboda, NilsOliver Linden, Ulrich Schollwöck and Claudius Hubig: Time Evolution for MatrixProduct 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: WEHWorkshop Isolated Quantum ManyBody 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 SingleSite DMRG Algorithm with Subspace Expansion
 09/2014: Munich Quantum Day: Claudius Hubig, F. Alexander Wolf and Ulrich Schollwöck: Algorithmic Advancements in DMRG
Workshops Coorganised

01/2019: Quantum Emitters in NonConventional Baths at MPQ Garching
together with Ignacio Cirac and Eduardo SanchezBurillo 
06/2016: First International ExQM Workshop at Lake Chiemsee
with the ExQM graduate school
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)
Awards
 Arnold Sommerfeld PhD Prize, 2017
Arnold Sommerfeld Center, LMU Munich  Deutschlandstipendium, 2011/2012
TU Berlin & Robert Bosch GmbH
CV
 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: SymmetryProtected 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.