Absence of spin liquid in non-frustrated correlated systems

TL;DR

This study investigates the possibility of a spin liquid phase in the non-frustrated half-filled Hubbard model on the honeycomb lattice, concluding that no spin liquid exists due to magnetic ordering occurring before the Mott transition.

Contribution

The paper demonstrates that previous claims of a spin liquid phase in this system are likely due to insufficient bath orbital modeling, providing a more accurate analysis with multiple bath orbitals.

Findings

No spin liquid phase is found; magnetic order occurs before the Mott transition.

Using multiple bath orbitals per boundary site is crucial for correct results.

The system is gapped only when magnetic order sets in, not in a spin liquid state.

Abstract

The question of the existence of a spin liquid state in the half-filled Hubbard model on the honeycomb (aka graphene) lattice is revisited. The Variational Cluster Approximation (VCA), the Cluster Dynamical Mean Field Theory (CDMFT) and the Cluster Dynamical Impurity Approximation (CDIA) are applied to various cluster systems. Assuming that the spin liquid phase coincides with the Mott insulating phase in this non-frustrated system, we find that the Mott transition is pre-empted by a magnetic transition occuring at a lower value of the interaction $U$, and therefore the spin liquid phase does not occur. This conclusion is obtained using clusters with two bath orbitals connected to each boundary cluster site. We argue that using a single bath orbital per boundary site is insufficient and leads to the erroneous conclusion that the system is gapped for all nonzero values of $U$.