Bifurcating subsystem symmetric entanglement renormalization in two dimensions

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.

18 pages, 10 figures

References in corpus (6)

• Non-Abelian Anyons and Topological Quantum Computation
• Local stabilizer codes in three dimensions without string logical operators
• Tensor-entanglement renormalization group approach to 2D quantum systems
• Entanglement renormalization and topological order
• Exact entanglement renormalization for string-net models
• Symmetry protection of measurement-based quantum computation in ground states