Efficient bond-adaptive approach for finite-temperature open quantum dynamics using the one-site time-dependent variational principle for matrix product states

Simulating the non-perturbative and non-Markovian dynamics of open quantum systems is a very challenging many body problem, due to the need to evolve both the system and its environments on an equal footing. Tensor network and matrix product states (MPS) have emerged as powerful tools for open system models, but the numerical resources required to treat finite-temperature environments grow extremely rapidly and limit their applications. In this study we use time-dependent variational evolution of MPS to explore the striking theory of Tamascelli et al. (Phys. Rev. Lett. 2019, 123, 090402.) that shows how finite-temperature open dynamics can be obtained from zero temperature, i.e., pure wave function, simulations. Using this approach, we produce a benchmark dataset for the dynamics of the Ohmic spin-boson model across a wide range of coupling strengths and temperatures, and also present a detailed analysis of the numerical costs of simulating non-equilibrium steady states, such as those emerging from the non-perturbative coupling of a qubit to baths at different temperatures. Despite ever-growing resource requirements, we find that converged non-perturbative results can be obtained, and we discuss a number of recent ideas and numerical techniques that should allow wide application of MPS to complex open quantum systems.

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Using Matrix-Product States for Open Quantum Many-Body Systems: Efficient Algorithms for Markovian and Non-Markovian Time-Evolution

Entropy ◽

10.3390/e22090984 ◽

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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Large-Scale Quantum Dynamics with Matrix Product States

Journal of Chemical Theory and Computation ◽

10.1021/acs.jctc.9b00301 ◽

2019 ◽

Vol 15 (6) ◽

pp. 3481-3498 ◽

Cited By ~ 20

Author(s):

Alberto Baiardi ◽

Markus Reiher

Keyword(s):

Quantum Dynamics ◽

Large Scale ◽

Matrix Product ◽

Matrix Product States

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Simulation of Matrix Product States For Dissipation and Thermalization Dynamics of Open Quantum Systems

Journal of Physics Communications ◽

10.1088/2399-6528/ab6141 ◽

2020 ◽

Vol 4 (1) ◽

pp. 015002 ◽

Cited By ~ 1

Author(s):

Souvik Agasti

Keyword(s):

Open Quantum Systems ◽

Quantum Systems ◽

Matrix Product ◽

Matrix Product States ◽

Open Quantum

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On the Existence and Robustness of Steady Position-Momentum Correlations for Time-Dependent Quadratic Systems

Advances in Mathematical Physics ◽

10.1155/2012/731602 ◽

2012 ◽

Vol 2012 ◽

pp. 1-16

Author(s):

M. Gianfreda ◽

G. Landolfi

Keyword(s):

Quantum Dynamics ◽

Quantum Correlations ◽

Time Dependent ◽

Quantum Decoherence ◽

Linear Superposition ◽

Time Intervals ◽

One Dimensional ◽

The One ◽

Basic Features ◽

Hamiltonian Operators

We discuss conditions giving rise to stationary position-momentum correlations among quantum states in the Fock and coherent basis associated with the natural invariant for the one-dimensional time-dependent quadratic Hamiltonian operators such as the Kanai-Caldirola Hamiltonian. We also discuss some basic features such as quantum decoherence of the wave functions resulting from the corresponding quantum dynamics of these systems that exhibit no timedependence in their quantum correlations. In particular, steady statistical momentum averages are seen over well-defined time intervals in the evolution of a linear superposition of the basis states of modified exponentially damped mass systems.

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

10.33774/chemrxiv-2021-jwdb5 ◽

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.

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