Renormalization group approach to symmetry protected topological phases

Abstract

A defining feature of a symmetry protected topological phase (SPT) in one-dimension is the degeneracy of the Schmidt values for any given bipartition. For the system to go through a topological phase transition separating two SPTs, the Schmidt values must either split or cross at the critical point in order to change their degeneracies. A renormalization group (RG) approach based on this splitting or crossing is proposed, through which we obtain an RG flow that identifies the topological phase transitions in the parameter space. Our approach can be implemented numerically in an efficient manner, for example, using the matrix product state formalism, since only the largest first few Schmidt values need to be calculated with sufficient accuracy. Using several concrete models, we demonstrate that the critical points and fixed points of the RG flow coincide with the maxima and minima of the entanglement entropy, respectively, and the method can serve as a numerically efficient tool to analyze interacting SPTs in the parameter space.

5 pages, 3 figures

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• Multi-critical topological transition at quantum criticality
• Topological marker approach to an interacting Su-Schrieffer-Heeger model
• A supervised learning algorithm for interacting topological insulators based on local curvature
• Multicriticality in a one-dimensional topological band insulator
• Curvature function renormalisation, topological phase transitions and multicriticality
• Scaling behavior in a multicritical one-dimensional topological insulator