Critical crossover phenomena driven by symmetry-breaking defects at quantum transitions

TL;DR

This paper investigates how localized symmetry-breaking defects influence the critical behavior of quantum phase transitions in one-dimensional quantum Ising models, revealing notable crossover phenomena characterized by fidelity measures.

Contribution

It introduces a renormalization-group framework to analyze defect-induced crossover regimes at quantum critical points, supported by numerical simulations.

Findings

Defects induce significant crossover effects in ground-state properties.

Fidelity susceptibility diverges with system size within the crossover regime.

Outside the crossover, fidelity susceptibility remains finite.

Abstract

We study the effects of symmetry-breaking defects at continuous quantum transitions (CQTs), which may arise from localized external fields coupled to the order-parameter operator. The problem is addressed within renormalization-group (RG) and finite-size scaling frameworks. We consider the paradigmatic one-dimensional quantum Ising models at their CQT, in the presence of defects which break the global ${\mathbb Z}_2$ symmetry. We show that such defects can give rise to notable critical crossover regimes where the ground-state properties experience substantial and rapid changes, from symmetric conditions to symmetry-breaking boundaries. An effective characterization of these crossover phenomena driven by defects is achieved by analyzing the ground-state fidelity associated with small changes of the defect strength. Within the critical crossover regime, the fidelity susceptibility shows a power-law divergence when increasing the system size, related to the RG dimension of the defect strength; in contrast, outside the critical defect regime, it remains finite. We support the RG scaling arguments with numerical results.