scholarly journals Simulating open quantum dynamics with time-dependent variational matrix product states: Towards microscopic correlation of environment dynamics and reduced system evolution

2016 ◽  
Vol 93 (7) ◽  
Author(s):  
Florian A. Y. N. Schröder ◽  
Alex W. Chin
Keyword(s):  
Quantum Dynamics ◽  
Time Dependent ◽  
Matrix Product ◽  
Matrix Product States ◽  
System Evolution ◽  
Open Quantum ◽  
Variational Matrix

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 Parallel time-dependent variational principle algorithm for matrix product states

2020 ◽  
Vol 101 (23) ◽  
Author(s):  
Paul Secular ◽  
Nikita Gourianov ◽  
Michael Lubasch ◽  
Sergey Dolgov ◽  
Stephen R. Clark ◽  
...  
Keyword(s):  
Variational Principle ◽  
Time Dependent ◽  
Matrix Product ◽  
Matrix Product States ◽  
Parallel Time

scholarly journals Chebyshev matrix product states with canonical orthogonalization for spectral functions of strongly correlated systems

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

We propose a method to calculate the spectral functions of strongly correlated 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. We demonstrate for the first time that Chebyshev MPS can be used in quantum chemistry. We also caution the application for electron-phonon system with densed density of states.

scholarly journals Construction of variational matrix product states for the Heisenberg spin-1 chain

2020 ◽  
Vol 102 (8) ◽  
Author(s):  
Jintae Kim ◽  
Minsoo Kim ◽  
Naoki Kawashima ◽  
Jung Hoon Han ◽  
Hyun-Yong Lee
Keyword(s):  
Matrix Product ◽  
Heisenberg Spin ◽  
Matrix Product States ◽  
Variational Matrix

scholarly journals A new method to calculate ultrafast electron dynamics in molecules based on matrix product states

2019 ◽  
Vol 205 ◽  
pp. 03009
Author(s):  
Lars-Hendrik Frahm ◽  
Daniela Pfannkuche
Keyword(s):  
Wave Function ◽  
Time Dependent ◽  
New Method ◽  
Matrix Product ◽  
Product State ◽  
Electron Dynamics ◽  
Matrix Product States ◽  
Electronic Wave ◽  
Matrix Product State ◽  
Electronic Wave Function

We propose a new method to describe electron dynamics in molecules on the scale of femtoseconds. It is based on factorizing the electronic wave function into a matrix product state and using this factorization to solve the time dependent Schrodinger equation.

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