Tensor-Network Approaches to Counting Statistics for the Current in a Boundary-Driven Diffusive System

TL;DR

This paper demonstrates the application of tensor network algorithms, DMRG and TEBD, to compute the current statistics in a boundary-driven diffusive system, validating their effectiveness against analytical solutions and confirming the fluctuation theorem.

Contribution

It introduces tensor-network methods for counting statistics in out-of-equilibrium diffusive systems, showing their accuracy and applicability.

Findings

Numerical cumulant generating functions match analytical solutions.

Tensor-network algorithms validate the fluctuation theorem.

Effective computation of current statistics in boundary-driven systems.

Abstract

We apply tensor networks to counting statistics for the stochastic particle transport in an out-of-equilibrium diffusive system. This system is composed of a one-dimensional channel in contact with two particle reservoirs at the ends. Two tensor-network algorithms, namely, Density Matrix Renormalization Group (DMRG) and Time Evolving Block Decimation (TEBD), are respectively implemented. The cumulant generating function for the current is numerically calculated and then compared with the analytical solution. Excellent agreement is found, manifesting the validity of these approaches in such an application. Moreover, the fluctuation theorem for the current is shown to hold.