scholarly journals Time dynamics with matrix product states: Many-body localization transition of large systems revisited

2020 ◽  
Vol 101 (3) ◽  
Author(s):  
Titas Chanda ◽  
Piotr Sierant ◽  
Jakub Zakrzewski
Keyword(s):  
Matrix Product ◽  
Many Body ◽  
Localization Transition ◽  
Matrix Product States ◽  
Time Dynamics ◽  
Large Systems

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 Efficient DMFT impurity solver using real-time dynamics with matrix product states

2015 ◽  
Vol 92 (15) ◽  
Author(s):  
Martin Ganahl ◽  
Markus Aichhorn ◽  
Hans Gerd Evertz ◽  
Patrik Thunström ◽  
Karsten Held ◽  
...  
Keyword(s):  
Real Time ◽  
Matrix Product ◽  
Matrix Product States ◽  
Time Dynamics

scholarly journals Chebyshev Matrix Product States with Canonical Orthogonalization for Spectral Functions of Many-Body Systems

2021 ◽  
Author(s):  
Tong Jiang ◽  
Jiajun Ren ◽  
Zhigang Shuai
Keyword(s):  
Ab Initio ◽  
Excited States ◽  
Time Dependent ◽  
Matrix Product ◽  
Effective Hamiltonian ◽  
Many Body ◽  
Spectral Functions ◽  
Matrix Product States ◽  
Many Body Systems ◽  
First Time

We propose a method to calculate the spectral functions of many-body systems by Chebyshev expansion in the framework of matrix product states coupled with canonical orthogonalization (coCheMPS). The canonical orthogonalization can improve the accuracy and efficiency significantly because the orthogonalized Chebyshev vectors can provide an ideal basis for constructing the effective Hamiltonian in which the exact recurrence relation can be retained. In addition, not only the spectral function but also the excited states and eigen energies can be directly calculated, which is usually impossible for other MPS-based methods such as time-dependent formalism or correction vector. The remarkable accuracy and efficiency of coCheMPS over other methods are demonstrated by calculating the spectral functions of spin chain and ab initio hydrogen chain. For the first time we demonstrate that Chebyshev MPS can be used to deal with ab initio electronic Hamiltonian effectively. We emphasize the strength of coCheMPS to calculate the low excited states of systems with sparse discrete spectrum. We also caution the application for electron-phonon systems with dense density of states.

scholarly journals Many-body localization in large systems: Matrix-product-state approach

2021 ◽  
pp. 168437
Author(s):  
Elmer V.H. Doggen ◽  
Igor V. Gornyi ◽  
Alexander D. Mirlin ◽  
Dmitry G. Polyakov
Keyword(s):  
Matrix Product ◽  
Product State ◽  
Many Body ◽  
Matrix Product State ◽  
Large Systems

scholarly journals Many-Body Localization Implies that Eigenvectors are Matrix-Product States

2015 ◽  
Vol 114 (17) ◽  
Author(s):  
M. Friesdorf ◽  
A. H. Werner ◽  
W. Brown ◽  
V. B. Scholz ◽  
J. Eisert
Keyword(s):  
Matrix Product ◽  
Many Body ◽  
Matrix Product States
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