Comment on "Absence of spin liquid in non-frustrated correlated systems"

TL;DR

This paper critiques prior claims of a spin-liquid phase in the honeycomb Hubbard model, arguing that the observed gap is due to methodological artifacts rather than true Mott physics, thus challenging previous conclusions.

Contribution

It demonstrates that CDMFT schemes violate translation symmetry, causing artificial gaps, and clarifies that the previous observed gap does not indicate a spin-liquid phase.

Findings

Six bath levels per six-site cell are sufficient for short-range correlations.

The gap at small U is due to symmetry violation, not Mott physics.

CDMFT schemes are unsuitable for identifying spin-liquid phases on the honeycomb lattice.

Abstract

In a recent Letter, Hassan and S\'en\'echal [1] discussed the existence of a spin-liquid phase of the half-filled Hubbard model on the honeycomb lattice. Using schemes, such as the variational cluster approximation (VCA) and the cluster dynamical mean field theory (CDMFT) in combination with exact diagonalization (ED), they argued that a single bath orbital per site of the six-atom unit cell is insufficient and leads to the erroneous conclusion that the system is gapped for all nonzero values of the onsite Coulomb interaction $U$. In contrast, we point out here that, in the case of the honeycomb lattice, six bath levels per six-site unit cell are perfectly adequate for the description of short-range correlations. Instead, we demonstrate that it is the violation of long-range translation symmetry inherent in CDMFT-like schemes which opens a gap at Dirac points. The gap found at small $U$ therefore does not correspond to a Mott gap. As a result, present CDMFT schemes are not suitable for the identification of a spin-liquid phase on the honeycomb lattice. [1] S.R. Hassan and D. S\'en\'echal, Phys. Rev. Lett. 110, 096402 (2013).