The extended Hubbard model on a honeycomb lattice

TL;DR

This study uses quantum Monte Carlo simulations to explore the phase diagram of the extended Hubbard model on a honeycomb lattice, revealing that only s-wave pairing occurs and that a semi-metal phase prevents d-wave superconductivity.

Contribution

It provides the first comprehensive phase diagram of the extended Hubbard model on a honeycomb lattice considering all sign combinations of interactions, using sign-problem-free quantum Monte Carlo methods.

Findings

Semi-metal phase prevents d-wave superconductivity.

Only s-wave pairing is observed in the phase diagram.

The phase diagram is mapped for all sign combinations of U and V.

Abstract

The lack of both nesting and a van Hove singularity at half filling, together with the presence of Dirac cones makes the honeycomb lattice a special laboratory to explore strongly correlated phenomena. For instance, at zero temperature the repulsive [attractive] Hubbard model only undergoes a transition to an antiferromagnetic [$s$-wave superconducting degenerate with charge density wave (SC-CDW)] for sufficiently strong on-site coupling, $U/t\gtrsim 3.85$ [$U/t\lesssim -3.85$]; in between these, the system is a semi-metal, by virtue of the Dirac cones. The addition of an additional interaction, $V>0$ or $V<0$, between fermions in nearest neighbor orbitals should break the SC-CDW degeneracy giving rise to a phase diagram quite distinct from the one for the square lattice. Here we perform determinant quantum Monte Carlo simulations to investigate the whole phase diagram, covering the four combinations of signs of $U$ and $V$; the use of complex Hubbard-Stratonovich fields renders the region $|V|\leq |U|/3$ free from the `minus sign problem'. We calculate structure factors associated with different orderings, which, together with the double occupancy and the average sign allows us to map out the whole phase diagram. We have found that the SM phase forms a zone from which ordered phases are excluded, preventing the stabilization of a $d$-wave SC phase, i.e., only $s$-wave pairing is allowed.