Scaling of Loschmidt echo in boundary driven critical Z-3 Potts model

TL;DR

This paper investigates how boundary perturbations affect the Loschmidt echo in a critical Z-3 Potts model, revealing power-law and Kibble-Zurek scaling behaviors through extensive numerical simulations.

Contribution

It extends the understanding of boundary-driven quantum critical dynamics from the Ising model to the Z-3 Potts model, demonstrating similar scaling phenomena.

Findings

Power-law scaling of Loschmidt echo at long times post-quench

Scaling modifications under sinusoidal and triangular pulses due to Kibble-Zurek effect

Validation of boundary condition change interpretation beyond Ising models

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 $\mathbb{Z}_3$ 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 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 which indicate that under a sinusoidal or triangular pulse, scaling with time period is modified by Kibble-Zurek effect, 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.