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

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

2010-10-04

arxiv.org/abs/1010.0455v1

Physics

Condensed Matter

Strongly Correlated Electrons

9 pages, 3 figures

Scientific paper

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.

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