Bifurcating subsystem symmetric entanglement renormalization in two dimensions

TL;DR

This paper develops a specialized entanglement renormalization group method that preserves subsystem symmetry, classifies bifurcating fixed points in 2D topological phases, and explores their implications for phase classification.

Contribution

It introduces a new real-space RG approach that maintains subsystem symmetry and classifies all bifurcating fixed points in 2D subsystem SPT phases.

Findings

Square lattice cluster state is a quotient-bifurcating fixed point.

Yoshida's fractal spin liquid models are self-bifurcating fixed points.

Relevance for classifying and understanding subsystem SPT phases.

Abstract

We introduce the subsystem symmetry-preserving real-space entanglement renormalization group and apply it to study bifurcating flows generated by linear and fractal subsystem symmetry-protected topological phases in two spatial dimensions. We classify all bifurcating fixed points that are given by subsystem symmetric cluster states with two qubits per unit cell. In particular, we find that the square lattice cluster state is a quotient-bifurcating fixed point, while the cluster states derived from Yoshida's first order fractal spin liquid models are self-bifurcating fixed points. We discuss the relevance of bifurcating subsystem symmetry-preserving renormalization group fixed points for the classification and equivalence of subsystem symmetry-protected topological phases.