Relation between the noise correlations and the spin structure factor for Mott-insulating states in SU$(N)$ Hubbard models

TL;DR

This paper derives and numerically confirms a relation between noise correlations and the spin structure factor in SU(N) Hubbard models' Mott-insulating states, revealing a $(t/U)^2$ deviation scaling at strong interactions.

Contribution

It provides an explicit mathematical relation between noise correlations and the spin structure factor for SU(N) Hubbard models at any integer filling, supported by numerical and semi-analytic analysis.

Findings

The relation holds in the strong-interaction limit $U \,\gg\, t$.

Deviation scales as approximately $(t/U)^2$ for $ ho=1$.

Numerical confirmation using density-matrix renormalization-group method.

Abstract

It is well established that the noise correlations measured by time-of-flight imaging in cold-atom experiments, which correspond to the density-density correlations in the momentum space of trapped atomic gases, can probe the spin structure factor deep in the Mott-insulating regime of SU(2) Hubbard models. We explicitly derive the mathematical relation between the noise correlations and the spin structure factor in the strong-interaction limit of SU$(N)$ Hubbard models at any integer filling $\rho$. By calculating the ground states of one-dimensional SU$(N)$ Fermi-Hubbard models for $2\leq N\leq 6$ with use of the density-matrix renormalization-group method, we confirm the relation numerically in the regime of strong interactions $U \gg t$, where $U$ and $t$ denote the onsite interaction and the hopping energy. We show that the deviation between the actual noise correlations and those obtained from the spin structure factor scales as approximately $(t/U)^2$ for $\rho=1$ at intermediate and large lattice sizes on the basis of numeric and semi-analytic arguments.