More is uncorrelated: Tuning the local correlations of SU($N$) Fermi-Hubbard systems via controlled symmetry breaking

Abstract

Cold-atom experiments based on alkali-like atoms provide us with a tool to experimentally realize Hubbard models with a large number $N$ of components. The value of $N$ can be seen as a new handle to tune the properties of the system, leading to new physics both in the case of fully SU($N$) symmetric systems, or in the presence of controlled symmetry breaking. We focus on the Mott transition at global half filling and we characterize local correlations between particles through the \emph{inter-flavor mutual information}, an experimentally accessible quantity that rigorously measures the distance from the closest gaussian state, unveiling features that cannot be accessed by conventional probes of Mottness. We prove that these correlations are fully independent from local entanglement and quantum discord, and, using Dynamical Mean-Field Theory, we show that the SU(4) system has significantly smaller correlations than the SU(2) counterpart. In the atomic limit we prove that increasing $N$ further decreases the strength of the correlations. This suggests that a controlled reduction of the symmetry, reducing the number of effective components, can be used to enhance the degree of correlation. We confirm this scenario solving the model for $N=4$ and gradually breaking the symmetry via a Raman field, revealing an evolution from the SU(4) to the SU(2) Mott transition as the symmetry-breaking term increases, with a sudden recovery of the large correlations of the SU(2) model at weak Raman coupling in the Mott state. By further exploring the interplay between energy repulsion and the Raman field, we obtain a rich phase diagram with three different phases -- a metal, a band insulator, and a Mott insulator -- all coexisting at a single tricritical point.