Spatial Kibble-Zurek mechanism through susceptibilities: the inhomogeneous quantum Ising model case

TL;DR

This paper explores the spatial Kibble-Zurek mechanism in the inhomogeneous quantum Ising model, combining numerical, analytical, and theoretical approaches to understand phase transition behavior and critical point detection.

Contribution

It introduces a novel application of Kibble-Zurek theory to spatially inhomogeneous quantum systems, linking susceptibilities to phase transition analysis.

Findings

Extrema of magnetization derivatives locate the critical point.

Kibble-Zurek scaling predictions are verified in spatial quenches.

Analytical and numerical methods complement each other in studying inhomogeneous systems.

Abstract

We study the quantum Ising model in the transverse inhomogeneous magnetic field. Such a system can be approached numerically through exact diagonalization and analytically through the renormalization group techniques. Basic insights into its physics, however, can be obtained by adopting the Kibble-Zurek theory of non-equilibrium phase transitions to description of spatially inhomogeneous systems at equilibrium. We employ all these approaches and focus on derivatives of longitudinal and transverse magnetizations, which have extrema near the critical point. We discuss how these extrema can be used for locating the critical point and for verification of the Kibble-Zurek scaling predictions in the spatial quench.