Study of Loschmidt Echo for two-dimensional Kitaev model

TL;DR

This study investigates how the Loschmidt Echo behaves in a two-dimensional Kitaev model on a honeycomb lattice, revealing critical decay patterns near quantum critical points and scaling behaviors, with extensions to a one-dimensional case.

Contribution

It provides new insights into the decay and scaling of Loschmidt Echo in 2D and 1D Kitaev models, highlighting effects of quantum criticality on decoherence.

Findings

LE shows a sharp dip near AQCP

LE exhibits scaling behavior with system size

LE remains small in the gapless phase

Abstract

In this paper, we study the Loschmidt Echo (LE) of a two-dimensional Kitaev model residing on a honeycomb lattice which is chosen to be an environment that is coupled globally to a central spin. The decay of LE is highly influenced by the quantum criticality of the environmental spin model e.g., it shows a sharp dip close to the anisotropic quantum critical point (AQCP) of its phase diagram. The early time decay and the collapse and revival as a function of time at AQCP do also exhibit interesting scaling behavior with the system size which is verified numerically. It has also been observed that the LE stays vanishingly small throughout the gapless phase of the model. The above study has also been extended to the 1D Kitaev model i.e. when one of the interaction terms vanishes.