Renormalization group approach to symmetry protected topological phases

TL;DR

This paper introduces a renormalization group method based on Schmidt value behavior to efficiently identify topological phase transitions in one-dimensional symmetry protected topological phases, linking entanglement features to phase boundaries.

Contribution

It proposes a novel RG approach utilizing Schmidt value crossings and splittings to detect SPT phase transitions, compatible with matrix product state calculations.

Findings

RG flow identifies topological phase transitions and fixed points.

Critical points correspond to maxima of entanglement entropy.

Method is efficient for analyzing interacting SPTs.

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.