Title: A multisite decomposition of the tensor network path integrals

Abstract

Tensor network decompositions of path integrals for simulating open quantum systems have recently been proven to be useful. However, these methods scale exponentially with the system size. This makes it challenging to simulate the non-equilibrium dynamics of extended quantum systems coupled with local dissipative environments. In this work, we extend the tensor network path integral (TNPI) framework to efficiently simulate such extended systems. The Feynman–Vernon influence functional is a popular approach used to account for the effect of environments on the dynamics of the system. In order to facilitate the incorporation of the influence functional into a multisite framework (MS-TNPI), we combine a matrix product state (MPS) decomposition of the reduced density tensor of the system along the sites with a corresponding tensor network representation of the time axis to construct an efficient 2D tensor network. The 2D MS-TNPI network, when contracted, yields the time-dependent reduced density tensor of the extended system as an MPS. The algorithm presented is independent of the system Hamiltonian. We outline an iteration scheme to take the simulation beyond the non-Markovian memory introduced by solvents. Applications to spin chains coupled to local harmonic baths are presented; we consider the Ising, XXZ, and Heisenberg models, demonstratingmore » that the presence of local environments can often dissipate the entanglement between the sites. We discuss three factors causing the system to transition from a coherent oscillatory dynamics to a fully incoherent dynamics. The MS-TNPI method is useful for studying a variety of extended quantum systems coupled with solvents.« less

Authors:

Bose, Amartya  ^[1];

• Search DOE PAGES for author "Bose, Amartya"
• Search DOE PAGES for ORCID "0000-0003-0685-5096"

Walters, Peter L.  ^[2]

• Search DOE PAGES for author "Walters, Peter L."
• Search DOE PAGES for ORCID "0000-0001-5031-8840"

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+ Show Author Affiliations

1. Princeton University, NJ (United States)
2. University of California, Berkeley, CA (United States)

Publication Date:

Mon Jan 10 00:00:00 EST 2022

Research Org.:

Princeton Univ., NJ (United States)

Sponsoring Org.:

USDOE Office of Science (SC); Miller Institute for Basic Research in Science

OSTI Identifier:

1978989

Alternate Identifier(s):

OSTI ID: 1839175

Grant/Contract Number:  

SC0019394

Resource Type:

Accepted Manuscript

Journal Name:

Journal of Chemical Physics

Additional Journal Information:

Journal Volume: 156; Journal Issue: 2; Journal ID: ISSN 0021-9606

Publisher:

American Institute of Physics (AIP)

Country of Publication:

United States

Language:

English

Subject:

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Heisenberg model; Ising spins; quantum mechanical systems and processes; tensor network theory; matrix product state; quantum dissipation; open quantum systems; density-matrix; Feynman path integral; statistical mechanics models