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.
Topological Defect Formation Beyond the Kibble-Zurek Mechanism in Crossover Transitions with Approximate Symmetries
Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University（上海交大物理与天文学院）；Shanghai Research Center for Quantum Sciences（上海量子科学研究中心）；Center for Nuclear Theory, Department of Physics and Astronomy, Stony Brook University（石溪大学物理与天文系核理论中心）
Rare Events Govern Defect Formation under Weak Symmetry Breaking
Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院斐兹克量子中心）；Shanghai Research Center for Quantum Sciences（上海量子科学研究中心）；Department of Physics, The Chinese University of Hong Kong（香港中文大学物理系）；The state Key Laboratory of Quantum Information Technologies and Materials, The Chinese University of Hong Kong（香港中文大学量子信息技术与材料国家重点实验室）
Irreversibility and symmetry breaking in the creation and annihilation of defects in active living matter
Zuckerberg Institute for Water Research, The Jacob Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev（本-古里安大学）；The Department of Physics, Ben-Gurion University of the Negev（本-古里安大学）；The Swiss Institute for Dryland Environmental and Energy Research, The Jacob Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev（本-古里安大学）；Department of Theoretical Physics, University of Geneva（日内瓦大学）；Department of Mathematics, Bar-Ilan University（巴伊兰大学）
Symmetry-breaking line defects embedded to a 3D $O(N)$ critical bulk
Fudan University（复旦大学）；Hong Kong University of Science and Technology（香港科技大学）；Hunan University（湖南大学）；Hefei National Laboratory（合肥国家实验室）；Westlake Institute for Advanced Study（西湖高等研究院）；Westlake University（西湖大学）
