Energy transport in Z3 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 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 γ as a function of Θ at different f/J. The estimated γ(f/J,Θ) point to a ballistic energy transport along a line of integrable points f=Jcos{3Θ} 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.