Fermionic Symmetry-Protected Topological Phase in a Two-Dimensional Hubbard Model

TL;DR

This paper demonstrates that a decorated honeycomb lattice Hubbard model hosts a two-dimensional fermionic symmetry-protected topological phase, characterized by nontrivial reflection symmetry and protected by time-reversal symmetry, distinct from free-fermion topological phases.

Contribution

It identifies a new fermionic SPT phase in a 2D Hubbard model on a decorated honeycomb lattice, linking it to a quantum disordered ground state of a mapped compass model.

Findings

Hubbard model maps to a quantum compass model on decorated lattices.

On the honeycomb lattice, the ground state is a nontrivial fermionic SPT phase.

The phase is protected by time-reversal and reflection symmetries.

Abstract

We study the two-dimensional (2D) Hubbard model using exact diagonalization for spin-1/2 fermions on the triangular and honeycomb lattices decorated with a single hexagon per site. In certain parameter ranges, the Hubbard model maps to a quantum compass model on those lattices. On the triangular lattice, the compass model exhibits collinear stripe antiferromagnetism, implying $d$-density wave charge order in the original Hubbard model. On the honeycomb lattice, the compass model has a unique, quantum disordered ground state that transforms nontrivially under lattice reflection. The ground state of the Hubbard model on the decorated honeycomb lattice is thus a 2D fermionic symmetry-protected topological phase. This state -- protected by time-reversal and reflection symmetries -- cannot be connected adiabatically to a free-fermion topological phase.