Study of Loschmidt Echo for a qubit coupled to an XY-spin chain environment

TL;DR

This paper investigates how the Loschmidt echo of a qubit coupled to a transverse XY spin chain behaves near critical and multicritical points, revealing faster decay and different scaling laws, with implications for decoherence.

Contribution

It provides a detailed analysis of Loschmidt echo dynamics near critical points in a spin chain environment, highlighting differences in scaling and decay close to multicritical points.

Findings

Faster decay of LE near multicritical points

Distinct scaling of collapse and revival times compared to quantum critical points

LE scaling near gapless critical lines is governed by multicritical points

Abstract

We study the temporal evolution of a central spin-1/2 (qubit) coupled to the environment which is chosen to be a spin-1/2 transverse XY spin chain. We explore the entire phase diagram of the spin-Hamiltonian and investigate the behavior of Loschmidt echo(LE) close to critical and multicritical point(MCP). To achieve this, the qubit is coupled to the spin chain through the anisotropy term as well as one of the interaction terms. Our study reveals that the echo has a faster decay with the system size (in the short time limit) close to a MCP and also the scaling obeyed by the quasiperiod of the collapse and revival of the LE is different in comparison to that close to a QCP. We also show that even when approached along the gapless critical line, the scaling of the LE is determined by the MCP where the energy gap shows a faster decay with the system size. This claim is verified by studying the short-time and also the collapse and revival behavior of the LE at a quasicritical point on the ferromagnetic side of the MCP. We also connect our observation to the decoherence of the central spin.