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arXiv:2512.03689

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

Edoardo Zavatti, Gabriele Bellomia, Matteo Ferraretto, Samuele Giuli, Massimo Capone

cond-mat.str-elcond-mat.quant-gasquant-phSubmitted Dec 3, 2025• Announced Dec 4, 2025• 0 citations• Revised Jan 7, 2026 (v2)
v1 · Dec 3, 2025v2 · Jan 7, 2026v3 · Mar 19, 2026
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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.

Comments
9 pages + references, 8 figures. Comments welcome!

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•Aug 28, 2020•0 citations
More is uncorrelated: Tuning the local correlations of SU(NNN) Fermi-Hubbard systems via controlled symmetry breaking
Cold-atom experiments based on alkali-like atoms provide us with a tool to experimentally realize Hubbard models with a large number NNN of components. The value of NNN 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(NNN) 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 NNN 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=4N=4N=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.
The advent of ultracold alkaline-earth atoms in optical lattices has established a platform for investigating correlated quantum matter with SU(NNN) symmetry, offering highly tunable model parameters that allow experiments to access phenomena that are unavailable in conventional materials. Understanding the ground-state physics of SU(NNN) Fermi-Hubbard models away from the Heisenberg limit and from the spin-flavor balanced setting is important, as examining the flavor imbalance reveals new physics in Fermi-Hubbard models and shows how SU(NNN) phases react to practical experimental imperfections in optical lattices. In this study, mean-field phase diagrams are presented for the unit-density SU(3) Fermi-Hubbard model at two sets of flavor densities, (13−δ,13+δ,13)\left(\tfrac{1}{3}-δ,\tfrac{1}{3}+δ,\tfrac{1}{3}\right)(31​−δ,31​+δ,31​) and (14−δ,14+δ,12)\left(\tfrac{1}{4}-δ,\tfrac{1}{4}+δ,\tfrac{1}{2}\right)(41​−δ,41​+δ,21​), with the flavor imbalance introduced as δδδ. Novel phases are identified at moderate interaction strengths for both densities and their robustness is investigated in the presence of flavor imbalance. Furthermore, we provide microscopic explanations of the phases found and their stability. Analysis of thermal ensembles of random mean-field solutions indicate that, at temperatures accessible in state-of-the-art cold atom experiments, some spin orders are hard for conventional scattering or local observable measurements to detect, but can be more accessible with quantum gas microscopy in optical lattice experiments. This work also shows that nesting and Mottness, intertwined in the usual SU(2) Hubbard model in stark contrast to generic materials, can be tuned in the SU(3) model and play distinct roles. The resulting phase diagrams not only deepen our understanding of SU(NNN) Fermi-Hubbard models but also inform future experimental search for new phases.
We study the thermodynamic properties of four-component fermionic mixtures described by the Hubbard model using the dynamical mean-field-theory approach. Special attention is given to the system with SU(4)-symmetric interactions at half filling, where we analyze equilibrium many-body phases and their coexistence regions at nonzero temperature for the case of simple cubic lattice geometry. We also determine the evolution of observables in low-temperature phases while lowering the symmetry of the Hamiltonian towards the two-band Hubbard model. This is achieved by varying interflavor interactions or by introducing the spin-flip term (Hund's coupling). By calculating the entropy for different symmetries of the model, we determine the optimal regimes for approaching the studied phases in experiments with ultracold alkali and alkaline-earth-like atoms in optical lattices.
The enhancement of the spin-space symmetry from the usual SU(2)\mathrm{SU}(2)SU(2) to SU(N)\mathrm{SU}(N)SU(N) with N>2N>2N>2 is promising for finding nontrivial quantum spin liquids, but the realization of SU(N)\mathrm{SU}(N)SU(N) spin systems in real materials is still challenging. Although there is a proposal in cold atomic systems, in magnetic materials with a spin-orbital degree of freedom it is difficult to achieve the SU(N)\mathrm{SU}(N)SU(N) symmetry by fine tuning. Here we propose a new mechanism by which the SU(4)\mathrm{SU}(4)SU(4) symmetry emerges in the strong spin-orbit coupling limit. In d1d^1d1 transition metal compounds with edge-sharing anion octahedra, the spin-orbit coupling gives rise to strongly bond-dependent and apparently SU(4)\mathrm{SU}(4)SU(4)-breaking hopping between the Jeff=3/2J_\textrm{eff}=3/2Jeff​=3/2 quartets. However, in the honeycomb structure, a gauge transformation maps the system to an SU(4)\mathrm{SU}(4)SU(4)-symmetric Hubbard model, which means that the system has a hidden symmetry in spite of its large spin-orbit coupling. In the strong repulsion limit at quarter filling, as expected in ααα-ZrCl3,_3,3​, the low-energy effective model is the SU(4)\mathrm{SU}(4)SU(4) Heisenberg model on the honeycomb lattice, which cannot have a trivial gapped ground state and is expected to host a gapless spin-orbital liquid. In such quantum spin-orbital liquids, both the spin and orbital degrees of freedom become fractionalized and correlated together at low temperature due to the strong frustrated interactions between them. Similarly to spinons in pure quantum spin liquids, quantum spin-orbital liquids can host not only spinon excitations, but also fermionic "orbitalon" excitations at low temperature, which we have named here in distinction from orbitons in the symmetry-broken Jahn-Teller phases.
We develop a self-consistent variant of the constrained path quantum Monte Carlo approach which ensures its independence of the trial wave function, and apply the method to compute ground-state correlations in the two-dimensional SU(3) Fermi-Hubbard Hamiltonian at 13\frac{1}{3}31​ filling, modeling fermions with three possible spin flavors moving on a square lattice with an average of one particle per site. We provide clear evidence of a quantum critical point separating a nonmagnetic uniform metallic phase from a regime where long-range ``spin'' order is present. This discovery of multiple successive transitions to magnetic states with regular, long-range alternation of the different flavors, whose symmetry changes as the interaction strength increases, significantly extends previous work in the Heisenberg limit to itinerant fermions. In addition to the rich quantum magnetism, this important physical system allows one to study integer filling and the associated Mott transition disentangled from nesting, in contrast to the usual SU(2) model, while preserving the square-lattice geometry. Our results also provide a significant step towards the interpretation of present and future experiments on fermionic alkaline-earth atoms, and other realizations of SU(N)\mathrm{SU}(N)SU(N) physics.
Ultracold alkaline-earth atoms and molecules now enable experimental realizations of SU(N)-symmetric Fermi-Hubbard models, yet theoretical understanding of these systems, particularly at finite doping remains limited. Here we investigate the strong-coupling limit of the SU(3) symmetric Fermi-Hubbard model on the triangular lattice across the full doping range. Using a three-flavor extension of Gutzwiller-projected hidden fermion determinant states (G-HFDS), a neural network based variational ansatz, we analyze two- and three-point spin-spin and spin-spin-hole correlations of the SU(3) Cartan generators. We further study the structure of a pair of doped holes for large periodic systems, and compare our results to the paradigmatic SU(2) square lattice equivalent, finding strikingly similar magnetic correlations, non-s-wave pairing symmetry, and enhanced binding energies. Our results provide a foundation for future exploration of doped SU(N) Mott insulators, providing insights for both theoretical developments and quantum simulation experiments.
This thesis reports original research on strongly interacting fermions described by Hubbard-like models which can be realized with ultracold atom experiments. In particular, two main directions have been pursued: (i) the control of magnetic and topological properties in a honeycomb lattice through a suitable tuning of the trapping potential, and (ii) the possibility to observe orbital-selective Mott physics in a multicomponent Fermi system where the SU(N) symmetry is broken in a controlled way. The first line of research is based on the idea that increasing the strength of a trapping potential, one can trap a strongly interacting fermions in a limited portion of space, thereby changing their average density and the related magnetic properties. In particular it was demonstrated that this confinement protocol can be used to designeffective “nanoflakes” which are reminiscent of a solid-state proposal [1]. The second step was to extend the same philosophy to the so-called Kane-Mele model, a spinful version of the paradigmatic model proposed by Haldane which presents quantum Hall states. This model can be realized with cold-atom systems using artificial gauge fields. In this thesis we consider a Kane-Mele-Hubbard model where the electronic structure of the Kane-Mele model is supplemented by the onsite Hubbard interaction, allowing us to study the interplay between the correlations and magnetism induced by the repulsion, with the non-trivial topological properties. Also for this model, we follow the strategy discussed above, namely the possibility to engineer an effective “nanoflake” by tuning the lattice potential. The final outcome in this case is even reacher, because it leads, among other results, to a situation where the effective flake hosts an inhomogeneous state which presents at the same time topologically non-trivial properties and magnetism, realizing a spin-Chern insulator [2]. Besides the remarkable application for topological matter, artificial gauge fields, which rely on the coupling of spin states, offer also great insides into mutli-orbital physics. In the second main research line reported in the thesis we study in collaboration with the experimental group of Leonardo Fallani, the controlled symmetry breaking on a 173Yb many-body system, where coupling between spin states is exploited to simulate the mechanism relevant for the physics of multi-orbital materials, such as iron-based superconductors. In order to reveal this mechanism in cold atoms we focus on interacting SU(3) lattice fermions where the SU(3) spin symmetry is explicitly broken by a Raman coupling between the spin states. Combining experiments and theory, we demonstrate that this setup reveals orbital-selective physics and it shows that the SU(3)-symmetry-breaking Raman coupling favours Mott localization and selective properties [3]. Our results show a clear evidence of orbital-selective correlations, which reflect in contrasting transport properties in different orbitals, the extreme case being an orbital-selective Mott state where only some of the orbitals are Mott localized while others remain metallic. Moreover, the coupling between spin states favors Mott localization with respect to the symmetric case, hence it reduces the critical interaction needed for a full Mott localization.