Tensor-Network Approach to Work Statistics for 1D Quantum Lattice Systems

TL;DR

This paper presents a tensor-network based numerical method combining TEBD and METTS to compute work statistics in 1D quantum lattice systems, enabling tests of quantum fluctuation relations.

Contribution

It introduces a novel combination of TEBD and METTS techniques for calculating work statistics in 1D quantum systems at finite temperature.

Findings

Successfully applied to the Ising chain in mixed fields

Able to compute work moments and test quantum Jarzynski equality

Adapted to verify universal quantum work relations

Abstract

We introduce a numerical approach to calculate the statistics of work done on 1D quantum lattice systems initially prepared in thermal equilibrium states. This approach is based on two tensor-network techniques: Time Evolving Block Decimation (TEBD) and Minimally Entangled Typical Thermal States (METTS). The former is an efficient algorithm used to simulate the dynamics of 1D quantum lattice systems, while the latter a finite-temperature algorithm for generating a set of typical states representing the Gibbs canonical ensemble. As an illustrative example, we apply this approach to the Ising chain in mixed transverse and longitudinal fields. Under an arbitrary protocol, the moment generating function of the work can be obtained, from which the work moments are numerically calculated and the quantum Jarzynski equality can be tested. Moreover, the numerical approach is also adapted to test the universal quantum work relation involving a functional of an arbitrary observable.