Tensor network methods for quantum many-body simulations

Erstveröffentlichung
2021-05-12Authors
Gerster, Matthias
Referee
Montangero, SimoneRizzi, Matteo
Dissertation
Faculties
Fakultät für NaturwissenschaftenInstitutions
Institut für Komplexe QuantensystemeAbstract
In this thesis, quantum many-body systems are studied by means of tensor network methods. After introducing the quantum many-body problem and discussing paradigmatic models as well as established methods for their solution, the focus is set on a practical approach to tensor network methods, always keeping in mind the realistic numerical applicability of the tools devised. In order to achieve this objective, we focus on loop-free network geometries, which allow to boost the computational performance to the greatest possible extent. The developed algorithms are described and benchmarked in detail, starting from their elementary constituents, namely the multidimensional arrays called tensors which are at the heart of any tensor network algorithm. We then apply the developed simulation techniques to a diverse collection of quantum many-body models of current research interest. We are interested, in particular, in a characterization of the ground-state properties of these models, but we also investigate problems beyond the zero-temperature equilibrium setting, such as time evolution or finite-temperature behavior. Specifically, novel findings for the phase diagrams of the disordered Bose-Hubbard chain and of the Heisenberg chain with additional biquadratic interactions are presented, as well as compelling new evidence for the existence of fractional quantum Hall states in the interacting Harper-Hofstadter model.
Date created
2020
Cumulative dissertation containing articles
• M. Gerster, P. Silvi, M. Rizzi, R. Fazio, T. Calarco, and S. Montangero; Physical Review B 90, 125154 (2014); https://doi.org/10.1103/physrevb.90.125154
• P. Silvi, F. Tschirsich, M. Gerster, J. Jünemann, D. Jaschke, M. Rizzi, and S. Montangero; SciPost Physics Lecture Notes 8 (2019); https://doi.org/10.21468/SciPostPhysLectNotes.8
• M. Gerster, M. Rizzi, F. Tschirsich, P. Silvi, R. Fazio, and S. Montangero; New Journal of Physics 18, 015015 (2016); http://iopscience.iop.org/article/10.1088/1367-2630/18/1/015015
• M. Gerster, M. Rizzi, P. Silvi, M. Dalmonte, and S. Montangero; Physical Review B 96, 195123 (2017); https://journals.aps.org/prb/abstract/10.1103/PhysRevB.96.195123
• M. Gerster, B. Haggenmiller, F. Tschirsich, P. Silvi, and S. Montangero; Physical Review B 100, 024311 (2019); https://journals.aps.org/prb/abstract/10.1103/PhysRevB.100.024311
• W. Weiss, M. Gerster, D. Jaschke, P. Silvi, and S. Montangero; Physical Review A 98, 063601 (2018); https://journals.aps.org/pra/abstract/10.1103/PhysRevA.98.063601
• P. Silvi, F. Tschirsich, M. Gerster, J. Jünemann, D. Jaschke, M. Rizzi, and S. Montangero; SciPost Physics Lecture Notes 8 (2019); https://doi.org/10.21468/SciPostPhysLectNotes.8
• M. Gerster, M. Rizzi, F. Tschirsich, P. Silvi, R. Fazio, and S. Montangero; New Journal of Physics 18, 015015 (2016); http://iopscience.iop.org/article/10.1088/1367-2630/18/1/015015
• M. Gerster, M. Rizzi, P. Silvi, M. Dalmonte, and S. Montangero; Physical Review B 96, 195123 (2017); https://journals.aps.org/prb/abstract/10.1103/PhysRevB.96.195123
• M. Gerster, B. Haggenmiller, F. Tschirsich, P. Silvi, and S. Montangero; Physical Review B 100, 024311 (2019); https://journals.aps.org/prb/abstract/10.1103/PhysRevB.100.024311
• W. Weiss, M. Gerster, D. Jaschke, P. Silvi, and S. Montangero; Physical Review A 98, 063601 (2018); https://journals.aps.org/pra/abstract/10.1103/PhysRevA.98.063601
Subject headings
[GND]: Quantentheorie | Computerphysik | Quantenphasenübergang | Vielkörperproblem[LCSH]: Quantum theory | Many-body problem
[Free subject headings]: Tensor networks | Quantum many-body problem
[DDC subject group]: DDC 530 / Physics
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Please use this identifier to cite or link to this item: http://dx.doi.org/10.18725/OPARU-37325
Gerster, Matthias (2021): Tensor network methods for quantum many-body simulations. Open Access Repositorium der Universität Ulm und Technischen Hochschule Ulm. Dissertation. http://dx.doi.org/10.18725/OPARU-37325
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