Topological phase transition between non-high symmetry critical phases and curvature function renormalization group

The interplay between topology and criticality has been a recent interest of study in condensed matter physics. A unique topological transition between certain critical phases has been observed as a consequence of the edge modes living at criticalities. In this work, we generalize this phenomenon by investigating possible transitions between critical phases which are non-high symmetry in nature. We find the triviality and non-triviality of these critical phases in terms of the decay length of the edge modes and also characterize them using the winding numbers. The distinct non-high symmetry critical phases are separated by multicritical points with linear dispersion at which the winding number exhibits the quantized jump, indicating a change in the topology (number of edge modes) at the critical phases. Moreover, we reframe the scaling theory based on the curvature function, i.e. curvature function renormalization group method to efficiently address the non-high symmetry criticalities and multicriticalities. Using this we identify the conventional topological transition between gapped phases through non-high symmetry critical points, and also the unique topological transition between critical phases through multicritical points. The renormalization group flow, critical exponents and correlation function of Wannier states enable the characterization of non-high symmetry criticalities along with multicriticalities.Comment: 12 pages + supplementary (4 pages), 13 figures. Comments are welcom

Unconventional quantum criticality in a non-Hermitian extended Kitaev chain

We investigate the nature of quantum criticality and topological phase transitions near the critical lines obtained for the extended Kitaev chain with next nearest neighbor hopping parameters and non-Hermitian chemical potential. We surprisingly find multiple gap-less points, the locations of which in the momentum space can change along the critical line unlike the Hermitian counterpart. The interesting simultaneous occurrences of vanishing and sign flipping behavior by real and imaginary components, respectively of the lowest excitation is observed near the topological phase transition. Introduction of non- Hermitian factor leads to an isolated critical point instead of a critical line and hence, reduced number of multi-critical points as compared to the Hermitian case. The critical exponents obtained for the multi-critical and critical points show a very distinct behavior from the Hermitian case.Comment: Suggestions and discussions are welcom

Topological phase transition at quantum criticality

Recently topological states of matter have witnessed a new physical phenomenon where both gapless edge and bulk excitations coexist. This manifests in the existence of exponentially localized edge modes living at certain criticalities with topological properties. The criticalities with topological and non-topological properties enable one to look into an unusual and interesting multicritical phenomenon: topological phase transition at criticality. We explore the existence of such topological transitions and reconstruct various suitable theoretical frameworks to characterize them. The bound state solution of Dirac equation and the winding number are constructed for the criticality to detect the multicritical points. We reframe the scaling theory of the curvature function and obtain the critical exponents to identify the topological transition between distinct critical phases separated by multicritical points. Finally, we discuss the experimental observabilities of our results in superconducting circuits and ultracold atoms.Comment: 6 pages + supplementary material; Extensively revised version, results unchange