scholarly journals Unifying time evolution and optimization with matrix product states

2016 ◽  
Vol 94 (16) ◽  
Author(s):  
Jutho Haegeman ◽  
Christian Lubich ◽  
Ivan Oseledets ◽  
Bart Vandereycken ◽  
Frank Verstraete
Keyword(s):  
Time Evolution ◽  
Matrix Product ◽  
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 Dynamical windows for real-time evolution with matrix product states

2013 ◽  
Vol 88 (3) ◽  
Author(s):  
Ho N. Phien ◽  
Guifré Vidal ◽  
Ian P. McCulloch
Keyword(s):  
Real Time ◽  
Time Evolution ◽  
Matrix Product ◽  
Matrix Product States

scholarly journals Time evolution of Matrix Product States

2006 ◽  
Vol 8 (12) ◽  
pp. 305-305 ◽  
Author(s):  
Juan José García-Ripoll
Keyword(s):  
Time Evolution ◽  
Matrix Product ◽  
Matrix Product States

scholarly journals Time-evolution methods for matrix-product states

2019 ◽  
Vol 411 ◽  
pp. 167998 ◽  
Author(s):  
Sebastian Paeckel ◽  
Thomas Köhler ◽  
Andreas Swoboda ◽  
Salvatore R. Manmana ◽  
Ulrich Schollwöck ◽  
...  
Keyword(s):  
Time Evolution ◽  
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
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