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

We study the effects of symmetry-breaking defects at continuous quantum transitions (CQTs) of homogeneous systems, 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 Z2 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 characterization of these crossover phenomena driven by defects. In particular, this is demonstrated 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.