Detecting the tunneling rates for strongly interacting fermions on optical lattices

TL;DR

This paper investigates how tunneling rates influence the phases of strongly interacting fermions in optical lattices, revealing a crossover driven by the particle-assisted tunneling rate g, with implications for experimental measurements.

Contribution

It introduces a Hubbard-like model with variable tunneling rates that reproduces the t-J Hamiltonian and identifies how g controls a crossover between different insulating phases.

Findings

g determines the transition from a paramagnetic to an antiferromagnetic insulator.

The model links the tunneling rate g to the superexchange interaction J.

Measurement of doubly occupied sites can estimate the effective tunneling rate g.

Abstract

Strongly interacting fermionic atoms on optical lattices are studied through a Hubbard-like model Hamiltonian, in which tunneling rates of atoms and molecules between neighboring sites are assumed to be different. In the limit of large onsite repulsion U, the model is shown to reproduce the t-J Hamiltonian, in which the J coefficient of the Heisenberg term depends on the particle-assisted tunneling rate g: explicitly, $J=4 g^2/U$. At half-filling, g drives a crossover from a Brinkman-Rice paramagnetic insulator of fully localized atoms (g=0) to the antiferromagnetic Mott insulator of the standard Hubbard case (g=t). This is observed already at the intermediate coupling regime in the number of doubly occupied sites, thus providing a criterion to extract from measurements the effective value of g.