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Time-evolution methods for matrix-product states
Univ Gottingen, Inst Theoret Phys, D-37077 Gottingen, Germany.
Univ Gottingen, Inst Theoret Phys, D-37077 Gottingen, Germany;.
Ludwig Maximilians Univ Munchen, Dept Phys, Arnold Sommerfeld Ctr Theoret Phys ASC, Fac Phys, D-80333 Munich, Germany.
Univ Gottingen, Inst Theoret Phys, D-37077 Gottingen, Germany.
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2019 (English)In: Annals of Physics, ISSN 0003-4916, E-ISSN 1096-035X, Vol. 411, article id 167998Article in journal (Refereed) Published
Abstract [en]

Matrix-product states have become the de facto standard for the representation of one-dimensional quantum many body states. During the last few years, numerous new methods have been introduced to evaluate the time evolution of a matrix-product state. Here, we will review and summarize the recent work on this topic as applied to finite quantum systems. We will explain and compare the different methods available to construct a time-evolved matrix-product state, namely the time-evolving block decimation, the MPO W-I,W-II method, the global Krylov method, the local Krylov method and the one- and two-site time-dependent variational principle. We will also apply these methods to four different representative examples of current problem settings in condensed matter physics. (C) 2019 The Author(s). Published by Elsevier Inc.

Place, publisher, year, edition, pages
ACADEMIC PRESS INC ELSEVIER SCIENCE , 2019. Vol. 411, article id 167998
Keywords [en]
Strongly-correlated systems, Matrix-product states (MPS), Time-evolution methods, Density matrix renormalization group (DMRG), Time-evolving block decimation (TEBD), Time-dependent variational principle (TDVP)
National Category
Other Physics Topics Computational Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-401171DOI: 10.1016/j.aop.2019.167998ISI: 000502886800036OAI: oai:DiVA.org:uu-401171DiVA, id: diva2:1383514
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EU, European Research Council, 742102EU, European Research Council, 758935Available from: 2020-01-08 Created: 2020-01-08 Last updated: 2020-01-08Bibliographically approved

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