Ultracold fermions and the SU(N) Hubbard model

TL;DR

This paper explores the phase behavior of the SU(N) Hubbard model on a 2D lattice using renormalization group and mean-field techniques, revealing various symmetry-breaking and ordering phenomena depending on N and filling.

Contribution

It provides new insights into the phase diagram of the SU(N) Hubbard model, including symmetry breaking, flux order, and pairing, especially for N>6 and away from half filling.

Findings

For N>6, staggered flux order dominates at half filling.

At small N, symmetry breaking is the main instability.

In the attractive case with odd N, coexistence of Fermi surface and superconductivity occurs.

Abstract

We investigate the fermionic SU(N) Hubbard model on the two-dimensional square lattice for weak to moderate interaction strengths using one-loop renormalization group and mean-field methods. For the repulsive case U>0 at half filling and small N the dominant tendency is towards breaking of the SU(N) symmetry. For N>6 staggered flux order takes over as the dominant instability, in agreement with the large-N limit. Away from half filling for N=3 the system rearranges the particle densities such that two flavors remain half filled by cannibalizing the third flavor. In the attractive case and odd N a full Fermi surface coexists with a superconductor in the ground state. These results may be relevant to future experiments with cold fermionic atoms in optical lattices.