Topological phase transition at quantum criticality

Recently, topological states of matter have witnessed a new physical phenomenon where gapless edge and bulk excitations coexist. This manifests in the existence of exponentially localized edge modes living at criticalities. The criticalities with topological and non-topological properties enable one to look into an unprecedented and interesting multicritical phenomenon: topological phase transition at criticality. We explore the existence of such topological transition between distinct critical phases of different topological nature and reconstruct various suitable theoretical frameworks to characterize them. The bound state solution of Dirac equation, winding number, scaling theory, critical exponents and correlation factors of curvature function are constructed at criticality to identify the topological transition between distinct critical phases separated by multicritical points. Finally, we discuss the experimental observabilities of these results in superconducting circuits and ultracold atoms.