Energy transport in chiral clock model

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 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 γ as a function of θ at different f / J . The estimated γ ( f / J , θ ) points to ballistic energy transport along a line of integrable points f = J cos 3 θ 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.

Keywords

• energy transport
• chiral clock model
• open quantum systems
• non equilibrium steady states
• integrability
• Potts model