Scaling of Loschmidt echo in a boundary-driven critical Z3 Potts model

Abstract

Low-frequency perturbations at the boundary of critical quantum chains can be understood in terms of the sequence of boundary conditions imposed by them, as has been previously demonstrated in the Ising and related fermion models. Using extensive numerical simulations, we explore the scaling behavior of the Loschmidt echo under longitudinal field perturbations at the boundary of a critical Z 3 Potts model. We show that at times much larger than the relaxation time after a boundary quench, the Loschmidt echo has a power-law scaling with time as expected from interpreting the quench as insertion of boundary condition changing operators. Similar scaling is observed as a function of time period under a low-frequency square-wave pulse. We present numerical evidence for one cycle that indicates that under a sinusoidal or triangular pulse, scaling with time period is modified by the Kibble-Zurek mechanism, again similar to the case of the Ising model. Results confirm the validity, beyond the Ising model, of the treatment of the boundary perturbations in terms of the effect on boundary conditions.