The scaling of the decoherence factor of a qubit coupled to a spin chain driven across quantum critical points

TL;DR

This paper investigates how the decoherence of a qubit coupled to a spin chain scales when the chain is driven across quantum critical points, revealing universal behavior and deviations along critical lines.

Contribution

It derives the scaling laws of the decoherence factor during non-equilibrium driving across quantum critical points, highlighting universality and differences from defect density scaling.

Findings

Scaling of decoherence matches defect density scaling for isolated critical points.

Deviations occur when driving along a critical line.

Analytical results agree with numerical simulations.

Abstract

We study the scaling of the decoherence factor of a qubit (spin-1/2) using the central spin model in which the central spin (qubit) is globally coupled to a transverse XY spin chain. The aim here is to study the non-equilibrium generation of decoherence when the spin chain is driven across (along) quantum critical points (lines) and derive the scaling of the decoherence factor in terms of the driving rate and some of the exponents associated with the quantum critical points. Our studies show that the scaling of logarithm of decoherence factor is identical to that of the defect density in the final state of the spin chain following a quench across isolated quantum critical points for both linear and non-linear variations of a parameter even if the defect density may not satisfy the standard Kibble-Zurek scaling. However, one finds an interesting deviation when the spin chain is driven along a critical line. Our analytical predictions are in complete agreement with numerical results. Our study, though limited to integrable two-level systems, points to the existence of a universality in the scaling of the decoherence factor which is not necessarily identical to the scaling of the defect density.