Building Symmetry Enriched Topological Phases from a Bipartite Lattice Construction and Anyon Condensation

TL;DR

This paper presents a novel method to construct symmetry-enriched topological phases on bipartite lattices by combining two $ ext{Z}_2$ spin liquids and condensing anyons, enabling the realization of diverse fractionalization patterns.

Contribution

It introduces a new lattice construction method for symmetry-enriched topological orders that includes states not easily achieved by traditional parton approaches.

Findings

Constructed featureless and topologically ordered states on honeycomb lattices.

Extended the construction to nonsymmorphic and magnetic translation symmetric lattices.

Discussed constraints on non-chiral topological orders in bosonic systems under magnetic fields.

Abstract

We introduce a construction of symmetry-enriched topological orders on bipartite lattices in which two $\mathbb{Z}_2$ spin liquids defined on each sublattice are combined, and then anyons are condensed to reduce the topological order. By choosing different anyon condensate structures, one can vary the fractionalization pattern of the resulting spin liquid, some of which cannot be readily constructed from parton based approaches. We demonstrate the construction for $i$) a spin-1/2 honeycomb lattice where we construct a featureless state as well as intermediate states with topological order, $ii$) a nonsymmorphic lattice, and $iii$) lattices with magnetic translation symmetry. At last, we discuss constraints on non-chiral topological orders in a bosonic system under magnetic field.