Energy transport in Z 3 chiral clock model

Abstract

We characterize the energy transport in a one dimensional Z3 chiral clock model. The model generalizes the Z2 symmetric Transverse Field Ising Model (TFIM). The model is parametrized by a chirality parameter θ, in addition to f and J which are analogous to the transverse field and the nearest neighbor spin coupling in the TFIM. Unlike the well-studied TFIM and XYZ models, this model 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 3 as a function of θ at different f/J. The estimated 3(f/J, θ) points to ballistic energy transport along a line of integrable points f = J cos 3θ in the parameter space; all other points deviate from ballistic transport. Analysis of finite size effects within the available system sizes suggest diffusive behavior away from the integrable points.