Searching for Topological Degeneracy in the Hubbard Model with Quantum Monte Carlo

TL;DR

This study uses quantum Monte Carlo to search for topological degeneracy in the Hubbard model on a honeycomb lattice, finding no evidence for such degeneracy up to 162 sites, thus challenging the presence of a topological spin liquid phase.

Contribution

It introduces a quantum Monte Carlo approach to detect topological degeneracy in the Hubbard model, providing a new method to identify topological spin liquids.

Findings

No evidence of topological degeneracy up to 162 sites

Topological degeneracy splitting decays exponentially with system size

Results suggest absence of a topological spin liquid phase in the studied parameter range

Abstract

Z2 spin liquids have topological order. One manifestation of this is that a Z2 spin liquid on a torus exhibits a four-fold degeneracy. Recent numerical evidence has argued for the existence of a spin liquid ground state in the Hubbard model on a honeycomb lattice near U approximately 4. The evidence for this claim involves the presence of a gapped state that lacks any identifiable order. This argument relies on being able to distinguish small order from no order which is notoriously difficult. In this paper we demonstrate an approach which uses quantum Monte Carlo to search for one of the key features that positively identify the topological spin liquid: the topological degeneracy. For any finite system, this topological degeneracy is split where the splitting decays exponentially with system size. We search for low lying states in the energy spectrum that could be identified as these topologically degenerate states. We show that, for system sizes up to N=162 sites, there is no evidence for these states being significantly below the first excited state giving evidence against the existence of a topological phase. We discuss the possible options for the Hubbard model on the honeycomb lattice in the absence of such degeneracy.