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

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.

9 pages, 3 figures

References in corpus (13)

• Non-Abelian Anyons and Topological Quantum Computation
• "Deconfined" quantum critical points
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Topological Mott Insulators
• Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions
• Spin-charge Separated Solitons in a Topological Band Insulator
• Global phase diagrams of frustrated quantum antiferromagnets in two dimensions: doubled Chern-Simons theory
• Quadrupolar correlations and spin freezing in S = 1 triangular lattice antiferromagnets
• Topological defects and the superfluid transition of the $s=1$ spinor condensate in two dimensions
• Mutual Chern-Simons theory for Z_2 topological order
• Dynamics and transport of the Z_2 spin liquid: application to kappa-(ET)2Cu2(CN)3
• Mutual-Chern-Simons effective theory of doped antiferromagnets
• Majorana liquids: the complete fractionalization of the electron

Cited by in corpus (19)

• Fermionic quantum criticality in honeycomb and $\pi$-flux Hubbard models: Finite-size scaling of renormalization-group-invariant observables from quantum Monte Carlo
• Phase Diagram of a Frustrated Quantum Antiferromagnet on the Honeycomb Lattice: Magnetic Order versus Valence-Bond Crystal formation
• Quantum phase transitions in the Kane-Mele-Hubbard model
• Magnetic order and paramagnetic phases in the quantum J1-J2-J3 honeycomb model
• The intermediate and spin-liquid phase of the half-filled honeycomb Hubbard model
• Symmetry-protected topological phases with charge and spin symmetries: response theory and dynamical gauge theory in 2D, 3D and the surface of 3D
• Phase Diagram of the Kane-Mele-Hubbard model
• Diagnosis of interaction-driven topological phase via exact diagonalization
• Unconventional Quantum Critical Points
• Quantum Phase Transitions around the Staggered Valence Bond Solid
• Majorana spin liquids and projective realization of SU(2) spin symmetry
• Cluster dynamical mean field theory of quantum phases on a honeycomb lattice
• Topological edge states of Kekulé-type photonic crystals induced by a synchronized rotation of unit cells
• Exotic continuous quantum phase transition between Z2 topological spin liquid and Neel order
• Quantum spin liquid in a kagome lattice spin-1/2 XY model with four-site exchange
• The landscape of the Hubbard model
• Confinement-deconfinement interplay in quantum phases of doped Mott insulators
• Topological Quantum Liquids with Quaternion Non-Abelian Statistics
• Searching for Topological Degeneracy in the Hubbard Model with Quantum Monte Carlo