Energy transport in Z3 chiral clock model

TL;DR

This paper investigates energy transport in a one-dimensional Z3 chiral clock model, revealing ballistic transport at integrable points and diffusive behavior elsewhere, using matrix product states to analyze non-equilibrium steady states.

Contribution

It introduces a novel analysis of energy transport in the Z3 chiral clock model, highlighting the role of integrability and providing detailed scaling of energy currents.

Findings

Ballistic energy transport occurs along integrable lines in parameter space.

Non-integrable points exhibit diffusive energy transport.

Matrix product states effectively compute non-equilibrium steady states up to 48 sites.

Abstract

We characterize the energy transport in a one dimensional $\mathbb{Z}_3$ chiral clock model. The model generalizes the $\mathbb{Z}_2$ symmetric transverse field Ising model (TFIM). The model is parametrized by a chirality parameter $\theta$, in addition to $f$ and $J$ which are analogous to the transverse field and the nearest neighbour spin coupling in the TFIM. Unlike the well studied TFIM and XYZ models, does not transform to a fermionic system. We use a matrix product states implementation of the Lindblad master equation to obtain the non-equilibrium steady state (NESS) in systems of sizes up to $48$. We present the estimated NESS current and its scaling exponent $\gamma$ as a function of $\theta$ at different $f/J$. The estimated $\gamma(f/J,\theta)$ point to a ballistic energy transport along a line of integrable points $f=J\cos{3\theta}$ in the parameter space; all other points deviate from ballistic transport. Analysis of finite size effects within the available system sizes suggest a diffusive behavior away from the integrable points.