General Hubbard model for strongly interacting fermions in an optical lattice and its phase detection

TL;DR

This paper introduces a generalized Hubbard model for strongly interacting fermions in optical lattices, revealing phase diagram symmetries and proposing an experimental detection method for exotic phases.

Contribution

It derives a lattice resonance Hamiltonian for strongly interacting fermions and maps it to a generalized Hubbard model with particle-assisted tunneling, offering new insights into phase behavior.

Findings

Attractive and repulsive models share similar phase diagram complexity.

Proposes an experimental method to detect exotic superfluid/magnetic phases.

Establishes a symmetry-based mapping between different interaction regimes.

Abstract

Based on consideration of the system symmetry and its Hilbert space, we show that strongly interacting fermions in an optical lattice or superlattice can be generically described by a lattice resonance Hamiltonian. The latter can be mapped to a general Hubbard model with particle assisted tunneling rates. We investigate the model under population imbalance and show the attractive and the repulsive models have the same complexity in phase diagram under the particle-hole mapping. Using this mapping, we propose an experimental method to detect possible exotic superfluid/magnetic phases for this system.