Quantum Spin Hall, triplet Superconductor, and topological liquid on the honeycomb lattice

TL;DR

This paper classifies topological phases in the honeycomb lattice Hubbard model, revealing two distinct ground states with different symmetries and topological properties, linked to quantum spin Hall and triplet superconductivity.

Contribution

It introduces a classification of order parameters based on SO(4) symmetry, identifying two types of ground states with unique topological and symmetry characteristics.

Findings

Type A ground state is adjacent to a Z_2xZ_2 topological phase with mutual semion statistics.

Type B ground state is adjacent to a nonabelian SU(2) Chern-Simons phase.

Connections to quantum Monte Carlo simulations are discussed.

Abstract

We classify the order parameters on the honeycomb lattice using the SO(4) symmetry of the Hubbard model. We will focus on the topologically nontrivial quantum spin Hall order and spin triplet superconductor, which together belong to the (3, 3) representation of the SO(4). Depending on the microscopic parameters, this (3, 3) order parameter has two types of ground states with different symmetries: type A, the ground state manifold is [S^2xS^2]/Z_2; and type B, with ground state manifold SO(3)xZ_2. We demonstrate that phase A is adjacent to a Z_2xZ_2 topological phase with mutual semion statistics between spin and charge excitations, while phase B is adjacent to a nonabelian phase described by SU(2) Chern-Simons theory. Connections of our study to the recent quantum Monte Carlo simulation on the Hubbard model on the honeycomb lattice will also be discussed.