scholarly journals Matrix-product-states approach to Heisenberg ferrimagnetic spin chains

1997 ◽  
Vol 55 (6) ◽  
pp. R3336-R3339 ◽  
Author(s):  
A. K. Kolezhuk ◽  
H.-J. Mikeska ◽  
Shoji Yamamoto
Keyword(s):  
Spin Chains ◽  
Matrix Product ◽  
Matrix Product States

scholarly journals Matrix product states forsu(2) invariant quantum spin chains

2016 ◽  
Vol 2016 (8) ◽  
pp. 083101 ◽  
Author(s):  
Rubina Zadourian ◽  
Andreas Fledderjohann ◽  
Andreas Klümper
Keyword(s):  
Quantum Spin ◽  
Spin Chains ◽  
Matrix Product ◽  
Quantum Spin Chains ◽  
Matrix Product States ◽  
Invariant Quantum

scholarly journals Integrable open spin chains related to infinite matrix product states

2016 ◽  
Vol 93 (15) ◽  
Author(s):  
B. Basu-Mallick ◽  
F. Finkel ◽  
A. González-López
Keyword(s):  
Spin Chains ◽  
Infinite Matrix ◽  
Matrix Product ◽  
Matrix Product States

scholarly journals Integrable Matrix Product States from boundary integrability

2019 ◽  
Vol 6 (5) ◽  
Author(s):  
Balázs Pozsgay ◽  
Lorenzo Piroli ◽  
Eric Vernier
Keyword(s):  
Integrability Condition ◽  
Spin Chains ◽  
Matrix Product ◽  
Square Root ◽  
Reflection Equation ◽  
Matrix Product States ◽  
Root Relation ◽  
Integrable Spin ◽  
Explicit Representations ◽  
Integrable Spin Chains

We consider integrable Matrix Product States (MPS) in integrable spin chains and show that they correspond to “operator valued” solutions of the so-called twisted Boundary Yang-Baxter (or reflection) equation. We argue that the integrability condition is equivalent to a new linear intertwiner relation, which we call the “square root relation”, because it involves half of the steps of the reflection equation. It is then shown that the square root relation leads to the full Boundary Yang-Baxter equations. We provide explicit solutions in a number of cases characterized by special symmetries. These correspond to the “symmetric pairs” (SU(N),SO(N)) and (SO(N),SO(D)\otimes⊗SO(N-D)), where in each pair the first and second elements are the symmetry groups of the spin chain and the integrable state, respectively. These solutions can be considered as explicit representations of the corresponding twisted Yangians, that are new in a number of cases. Examples include certain concrete MPS relevant for the computation of one-point functions in defect AdS/CFT.

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.

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