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

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.

arXiv comment29 pages; 5 figures & 5 tables

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• Topological theory of Lieb-Schultz-Mattis theorems in quantum spin systems
• Relative Anomaly in (1+1)d Rational Conformal Field Theory
• Gapping fragile topological bands by interactions
• Nonlinear Symmetry-Fragmentation of Nonabelian Anyons In Symmetry-Enriched Topological Phases: A String-Net Model Realization