Responses for one-dimensional quantum spin systems via tensor networks

TL;DR

This paper develops tensor network methods to compute linear and nonlinear responses of one-dimensional quantum spin systems in thermal equilibrium, demonstrating accurate calculations on the Ising chain under external perturbations.

Contribution

It introduces a tensor network approach to evaluate responses in quantum spin chains, including exact calculations and response corrections for the first time.

Findings

Tensor networks effectively compute responses in quantum spin systems.

First and second-order responses accurately match exact calculations.

Response theory is extended to nontrivial quantum many-body systems.

Abstract

Tensor networks are adopted to calculate the responses for one-dimensional quantum spin systems that are initially in thermal equilibrium. The Ising chain in mixed transverse and longitudinal fields is used as the benchmarking system. The linear and second-order responses of the magnetization in $z$-direction induced by the time-dependent force conjugated with the magnetization in $x$-direction are calculated. In addition, the magnetization in $z$-direction is also exactly calculated in response to this excitation. As expected, the first two responses are shown to be excellent corrections to the equilibrium magnetization in $z$-direction when the excitation is weak. This result represents an illustrative example of the response theory for nontrivial quantum many-body systems.