Featureless quantum insulator on the honeycomb lattice

TL;DR

This paper constructs explicit examples of symmetric, gapped, non-topological quantum states on a honeycomb lattice for spin-1/2 particles using PEPS, demonstrating a featureless quantum insulator with no symmetry breaking.

Contribution

It provides the first explicit realization of a featureless quantum insulator for spin-1/2 particles on a honeycomb lattice using PEPS with a specific virtual bond dimension.

Findings

No topological degeneracy observed

Energy gap confirmed via numerical calculations

Four distinct classes based on lattice quantum numbers

Abstract

We show how to construct fully symmetric, gapped states without topological order on a honey- comb lattice for S = 1/2 spins using the language of projected entangled pair states(PEPS). An explicit example is given for the virtual bond dimension D = 4. Four distinct classes differing by lattice quantum numbers are found by applying the systematic classification scheme introduced by two of the authors [S. Jiang and Y. Ran, Phys. Rev. B 92, 104414 (2015)]. Lack of topological degeneracy or other conventional forms of symmetry breaking, and the existence of energy gap in the proposed wave functions, are checked by numerical calculations of the entanglement entropy and various correlation functions. Our work provides the first explicit realization of a featureless quantum insulator for spin-1/2 particles on a honeycomb lattice.