scholarly journals Time-dependent variational principle for mixed matrix product states in the thermodynamic limit

2020 ◽  
Vol 102 (13) ◽  
Author(s):  
Yantao Wu
Keyword(s):  
Variational Principle ◽  
Thermodynamic Limit ◽  
Time Dependent ◽  
Matrix Product ◽  
Mixed Matrix ◽  
Matrix Product States

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 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.

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 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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