Simulation of Spin Chains with off-diagonal Coupling Using Inchworm Method

TL;DR

This paper extends the inchworm method and tensor-train techniques to simulate open quantum spin chains with off-diagonal couplings, enabling efficient long-time dynamics simulations with reduced computational costs.

Contribution

The work generalizes the inchworm method and modular path integrals to off-diagonal couplings and integrates tensor-train and transfer tensor methods for efficient long-time simulation.

Findings

Validated the method with numerical experiments

Achieved reduced computational and memory costs

Successfully simulated long-time dynamics of spin chains

Abstract

We study the dynamical simulation of open quantum spin chain with nearest neighboring coupling, where each spin in the chain is associated with a harmonic bath. This is an extension of our previous work [G. Wang and Z. Cai, J. Chem. Theory Comput., 19, 8523--8540, 2023] by generalizing the application of the inchworm method and the technique of modular path integrals from diagonally coupled cases to off-diagonally coupled cases. Additionally, to reduce computational and memory cost in long time simulation, we apply tensor-train representation to efficiently represent the reduced density matrix of the spin chains, and employ the transfer tensor method (TTM) to avoid exponential growth of computational cost with respect to time. Abundant numerical experiments are performed to validate our method.