scholarly journals Lanczos algorithm with matrix product states for dynamical correlation functions

2012 ◽  
Vol 85 (20) ◽  
Author(s):  
P. E. Dargel ◽  
A. Wöllert ◽  
A. Honecker ◽  
I. P. McCulloch ◽  
U. Schollwöck ◽  
...  
Keyword(s):  
Correlation Functions ◽  
Matrix Product ◽  
Lanczos Algorithm ◽  
Dynamical Correlation ◽  
Matrix Product States

scholarly journals Reorthonormalization of Chebyshev matrix product states for dynamical correlation functions

2018 ◽  
Vol 97 (7) ◽  
Author(s):  
H. D. Xie ◽  
R. Z. Huang ◽  
X. J. Han ◽  
X. Yan ◽  
H. H. Zhao ◽  
...  
Keyword(s):  
Correlation Functions ◽  
Matrix Product ◽  
Dynamical Correlation ◽  
Matrix Product States

scholarly journals Dynamical correlation functions for products of random matrices

2015 ◽  
Vol 04 (04) ◽  
pp. 1550020 ◽  
Author(s):  
Eugene Strahov
Keyword(s):  
Random Matrices ◽  
Discrete Time ◽  
Random Matrix ◽  
Correlation Functions ◽  
Singular Values ◽  
Matrix Product ◽  
Dynamical Correlation ◽  
Products Of Random Matrices ◽  
Special Cases ◽  
Correlation Kernels

We introduce and study a family of random processes with a discrete time related to products of random matrices. Such processes are formed by singular values of random matrix products, and the number of factors in a random matrix product plays a role of a discrete time. We consider in detail the case when the (squared) singular values of the initial random matrix form a polynomial ensemble, and the initial random matrix is multiplied by standard complex Gaussian matrices. In this case, we show that the random process is a discrete-time determinantal point process. For three special cases (the case when the initial random matrix is a standard complex Gaussian matrix, the case when it is a truncated unitary matrix, or the case when it is a standard complex Gaussian matrix with a source) we compute the dynamical correlation functions explicitly, and find the hard edge scaling limits of the correlation kernels. The proofs rely on the Eynard–Mehta theorem, and on contour integral representations for the correlation kernels suitable for an asymptotic analysis.

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
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