Topological physics in quantum critical systems

Ruben Verresen, Nick G. Jones, Roderich Moessner +1 more

Kuang-Hung Chou, Xue-Jia Yu

Recent advances have revealed that topology can further enrich the universality classes of quantum phase transitions, thereby extending beyond the traditional paradigms of statistical and condensed matter physics. However, multicriticality between topologically distinct quantum critical lines remains insufficiently explored. In this Letter, we systematically construct and investigate a novel class of topologically enforced Lifshitz multicritical points in one dimensional chiral symmetric fermionic systems. Such multicriticality is driven solely by changes in the topology of neighboring critical lines, beyond previously recognized multicritical points that are typically induced by changes in critical exponents. More importantly, the topologically enforced multicriticality identified here can host robust topological degeneracies while surprisingly exhibiting a breakdown of the Li Haldane bulk boundary correspondence-a phenomenon we elucidate through a simple physical picture.

Yuxuan Guo, Sheng Yang, Xue-Jia Yu

Topological phenomena in quantum critical systems have recently attracted growing attention, as they go beyond the traditional paradigms of condensed matter and statistical physics. However, a general framework for identifying such nontrivial phenomena, particularly in higher-dimensional systems, remains insufficiently explored. In this work, we propose a universal fingerprint for detecting nontrivial topology in critical free-fermion systems protected by global on-site symmetries. Specifically, we analytically establish an exact relation between the bulk entanglement spectrum and the boundary energy spectrum at topological criticality in arbitrary dimensions, demonstrating that the degeneracy of edge modes can be extracted from the bulk entanglement spectrum. These findings, further supported by numerical simulations of lattice models, provide a universal fingerprint for identifying nontrivial topology in critical free-fermion systems.

Carlos M. Duque, Hong-Ye Hu, Yi‐Zhuang You +3 more

Topological phases represent a pillar of modern condensed matter physics. While gapped topological systems have been studied extensively, gapless topological materials represent an exciting, largely unexplored area. Here, the authors show that symmetry can enrich random quantum critical points and phases. They uncover a class of gapless topological phases, protected by symmetry and robust to strong randomness. Some of these phases can be realized in nonequilibrium states stabilized by many-body localization. They also appear naturally in periodically driven (Floquet) systems.

F. D. M. Haldane