Numerical studies of non-equilibrium dynamics in Z3 chiral clock model

Abstract

This thesis addresses the out-of-equilibrium physics of the one-dimensional Z3 chiral clock model. The model is the Z3 symmetric generalization of the quantum Ising model. Jordan-Wigner transformation maps the model to parafermions similar to the mapping to fermions of the Ising model, however, this does not make the model exactly solvable. The interplay of chirality, multiple domain wall flavors, and integrability of the chiral clock model reflects in the quantum dynamics; we explore this using the matrix product states technique. We drive the chiral clock model out of equilibrium through three different protocols - periodic boundary drive, quench, and through coupling to two thermal baths of unequal temperature. For the slow boundary periodic drive of the critical Z3 clock chain, we argue using the Kibble-Zurek mechanism and critical scaling properties that the Loschmidt echo scales with frequency as a power law whose exponent depends on the functional form of the boundary perturbation. We demonstrate this using large scale matrix product states calculations. For weak quenches from an ordered state, we showed that the system thermalizes in the bulk, but the boundary fails to thermalize in the chiral case but thermalizes in the non-chiral system. We present an understanding in terms of entanglement growth due to domain wall dynamics and scattering properties at the boundaries.Lastly, we present the energy transport properties of the model and explore its dependence on chirality. Non-equilibrium steady-state energy transport arising in response to a thermal gradient is modeled by using the Lindblad master equation implemented. We show that energy transport is ballistic at the integrable points and superdiffusive otherwise. In addition to the results on Z3 chiral clock model, we also discuss the temporal order observed in a nearly-Z2-symmetric realization of interacting spin-half degrees of freedom in an NMR system. The system shows robust period two response when driven out of equilibrium by approximate fi-pulse sequences.