Matrix Product States: Foundations

2015 ◽  
pp. 141-176
Author(s):  
Michael L. Wall
Keyword(s):  
Matrix Product ◽  
Matrix Product States

scholarly journals Optimal sampling of dynamical large deviations via matrix product states

2021 ◽  
Vol 103 (6) ◽  
Author(s):  
Luke Causer ◽  
Mari Carmen Bañuls ◽  
Juan P. Garrahan
Keyword(s):  
Large Deviations ◽  
Matrix Product ◽  
Optimal Sampling ◽  
Matrix Product States

scholarly journals Using Matrix-Product States for Open Quantum Many-Body Systems: Efficient Algorithms for Markovian and Non-Markovian Time-Evolution

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 984
Author(s):  
Regina Finsterhölzl ◽  
Manuel Katzer ◽  
Andreas Knorr ◽  
Alexander Carmele
Keyword(s):  
Time Evolution ◽  
Nearest Neighbor ◽  
Matrix Product ◽  
Body System ◽  
Many Body ◽  
Initial State ◽  
Matrix Product States ◽  
Open Quantum ◽  
Many Body Systems ◽  
The Many

This paper presents an efficient algorithm for the time evolution of open quantum many-body systems using matrix-product states (MPS) proposing a convenient structure of the MPS-architecture, which exploits the initial state of system and reservoir. By doing so, numerically expensive re-ordering protocols are circumvented. It is applicable to systems with a Markovian type of interaction, where only the present state of the reservoir needs to be taken into account. Its adaption to a non-Markovian type of interaction between the many-body system and the reservoir is demonstrated, where the information backflow from the reservoir needs to be included in the computation. Also, the derivation of the basis in the quantum stochastic Schrödinger picture is shown. As a paradigmatic model, the Heisenberg spin chain with nearest-neighbor interaction is used. It is demonstrated that the algorithm allows for the access of large systems sizes. As an example for a non-Markovian type of interaction, the generation of highly unusual steady states in the many-body system with coherent feedback control is demonstrated for a chain length of N=30.

scholarly journals Real time evolution at finite temperatures with operator space matrix product states

2014 ◽  
Vol 16 (7) ◽  
pp. 073007 ◽  
Author(s):  
Iztok Pižorn ◽  
Viktor Eisler ◽  
Sabine Andergassen ◽  
Matthias Troyer
Keyword(s):  
Real Time ◽  
Time Evolution ◽  
Operator Space ◽  
Matrix Product ◽  
Matrix Product States ◽  
Space Matrix

scholarly journals Matrix product states algorithms and continuous systems

2007 ◽  
Vol 75 (10) ◽  
Author(s):  
S. Iblisdir ◽  
R. Orús ◽  
J. I. Latorre
Keyword(s):  
Continuous Systems ◽  
Matrix Product ◽  
Matrix Product States
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