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

TL;DR

The paper investigates how local correlations in SU($N$) Hubbard models, realized in cold-atom platforms, depend on the number of flavors and symmetry breaking. It uses inter-flavor mutual information as an experimentally accessible, information-theoretic proxy for local correlations, and analyzes SU(2) versus SU(4) behavior with Dynamical Mean-Field Theory, complemented by the exactly solvable atomic limit. A Raman-induced symmetry-breaking term is shown to interpolate between SU(4) and SU(2) physics, producing flavor-selective Mott localization and a tricritical point in the $\Omega$-$U$ phase diagram. The results reveal that local correlations shrink with increasing $N$, while controlled symmetry breaking can enhance correlations and generate rich phase behavior, offering concrete experimental pathways in ultracold-atom simulators. Overall, the work links fermionic nongaussianity and classical local correlations to tangible many-body phases, informing both fundamental understanding and design of correlated quantum materials.

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.

Figures (8)

• Figure 1: (a) Schematic representation of an SU(4) lattice, with nearest neighbors hopping. Each site can host up to 4 flavors. (b) The inter-flavor energy repulsion, equal for each pair of flavors, is labeled by $U$, while $\Omega$ represents a flavor-selective Raman field, which acts essentially as an inter-flavor hopping. (c) The evolution of the flavored dispersions as a function of the Bethe half-bandwidth $D$, where the dashed line marks the Fermi level $E_\mathrm{F}$ and $\pm\Omega$ marks the Raman-induced split of the coupled flavors.
• Figure 2: Quasiparticle weight $Z_\alpha$ for the SU(2) and SU(4) Hubbard models as a function of $U/D$. The vanishing of $Z_\alpha$ marks the Mott transition.
• Figure 3: Two-flavor entropy $s_{12}$, single-flavor entropy $s_1=s_2$ and inter-flavor mutual information $I_{12}$, plotted against the interaction strength, for the SU($2$) Hubbard model (top panel) and the SU($4$) model (bottom panel). The area under the mutual information is shaded to indicate that all local correlators are contained beneath it.  All quantities are in units of $\log(2)$ (bits, in information theory language).
• Figure 4: Inter-flavor mutual information (top) and double occupancy per site (bottom) for a half-filled SU($N$) Hubbard model in the atomic limit $t=0$, plotted against the total number of flavors $N$. In the inset we show again the mutual information vs. $N$ in a log-log plot highlighting the $1/2N^2$ scaling (red dashed line).
• Figure 5: Double occupancies per site for the Raman-free flavors (top panel) and the Raman-coupled flavors (bottom panel) for different values of the Raman coupling $\Omega$. For Raman-coupled flavors, double occupancies vanish for $U > U^{\mathrm{R}}_{\mathrm{c}}(\Omega)$ due to the occurrence of complete polarization, while the Raman-free ones display a crossover between the values in the SU($4$) and SU($2$) Hubbard model.