Signatures of topological phase transition on a quantum critical line

Kumar, Ranjith R; Roy, Nilanjan; Kartik, Y R; Sinha, Rahul; Sarkar, Sujit

doi:10.1103/physrevb.107.205114

Cited by 10 publications

(14 citation statements)

References 51 publications

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“…The distinct HS critical phases are separated by the multicritical points and favor an unusual topological transition between them. This transition occurs without gap closing and opening at HS points in contrast to the conventional topological transition [26,31,32,40]. The multicritical points which favor the transition are found to have quadratic dispersion.…”

Section: Introductionmentioning

confidence: 76%

“…are the Pauli matrices. The model represents the 1D topological insulator and superconductor with extended nearest neighbor couplings [6,40,[44][45][46]. Topological distinct gapped phases of the model can be identified with the winding number…”

Section: Model and Topological Phase Diagrammentioning

confidence: 99%

“…Recently, this conventional understanding has been re-investigated and the edge modes are observed to be localized and stable even at certain critical points [28][29][30][31][32][33][34][35][36][37][38][39][40]. Therefore, similar to the gapped topological phases, certain critical phases also possess localized stable edge modes.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, similar to the gapped topological phases, certain critical phases also possess localized stable edge modes. The critical phases with topological and non-topological characters are identified as the high symmetry (HS) in nature since the gap closing occurs at the HS points in momentum space [40]. The distinct HS critical phases are separated by the multicritical points and favor an unusual topological transition between them.…”

Section: Introductionmentioning

confidence: 99%

“…In general, they are the intersection points of the distinct criticalities and are studied in different contexts [41][42][43]. The scaling theory developed to identify the topological transition between gapped phases, are reframed to identify the topological transition between HS critical phases [26,40]. The RG flow lines, correlation factors and decay length of edge modes at criticality, effectively characterized the topological transition [40].…”

Section: Introductionmentioning

confidence: 99%

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

2023

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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.

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Section: Introductionmentioning

confidence: 76%