The advent of ultracold alkaline-earth atoms in optical lattices has established a platform for investigating correlated quantum matter with SU( $N$ ) 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( $N$ ) 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( $N$ ) 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, $\left(\tfrac{1}{3}-δ,\tfrac{1}{3}+δ,\tfrac{1}{3}\right)$ and $\left(\tfrac{1}{4}-δ,\tfrac{1}{4}+δ,\tfrac{1}{2}\right)$ , with the flavor imbalance introduced as $δ$ . 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( $N$ ) Fermi-Hubbard models but also inform future experimental search for new phases.The advent of ultracold alkaline-earth atoms in optical lattices has established a platform for investigating correlated quantum matter with SU($N$) 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($N$) 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($N$) 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, $\left(\tfrac{1}{3}-δ,\tfrac{1}{3}+δ,\tfrac{1}{3}\right)$ and $\left(\tfrac{1}{4}-δ,\tfrac{1}{4}+δ,\tfrac{1}{2}\right)$, with the flavor imbalance introduced as $δ$. 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($N$) Fermi-Hubbard models but also inform future experimental search for new phases.

arXiv:2503.17776Physical Review AAug 25, 20251 citation

Higher-order correlations in the Fermi-Hubbard model

Annabelle Bohrdt, Joannis Koepsell, Dominik Bourgund +9 more

Bulletin of the American Physical SocietyMar 15, 20210 citations

High-temperature transport in the one-dimensional mass-imbalanced Fermi-Hubbard model

Thomas G. Kiely, Erich J. Mueller

We study transport in the one-dimensional mass-imbalanced Fermi-Hubbard model in the high-temperature limit, focusing on the case of strong interactions. Prior theoretical and experimental investigations have revealed unconventionally long transport timescales, with complications due to strong finite-size effects. We compute the dynamical current-current correlation function directly in the thermodynamic limit using infinite tensor network techniques. We show that transport in the strong-imbalance limit is dominated by AC resonances, which we compute with an analytic expansion. We study the dephasing of these resonances with mass imbalance, $\ensuremath{\eta}$. In the small-imbalance limit, the model is nearly integrable. We connect these unusual limits by computing the DC conductivity and transport decay time as a function of $\ensuremath{\eta}$ and the interaction strength $U/t$ . We propose an experimental protocol to measure these correlation functions in cold atom experiments.We study transport in the one-dimensional mass-imbalanced Fermi-Hubbard model in the high-temperature limit, focusing on the case of strong interactions. Prior theoretical and experimental investigations have revealed unconventionally long transport timescales, with complications due to strong finite-size effects. We compute the dynamical current-current correlation function directly in the thermodynamic limit using infinite tensor network techniques. We show that transport in the strong-imbalance limit is dominated by AC resonances, which we compute with an analytic expansion. We study the dephasing of these resonances with mass imbalance, $\ensuremath{\eta}$. In the small-imbalance limit, the model is nearly integrable. We connect these unusual limits by computing the DC conductivity and transport decay time as a function of $\ensuremath{\eta}$ and the interaction strength $U/t$. We propose an experimental protocol to measure these correlation functions in cold atom experiments.

arXiv:2404.08076Physical Review AJun 12, 20246 citations

Mass-imbalanced Hubbard model on a 2D square lattice

Amir Kaffashnia

The Hubbard model (HM) and the Falicov-Kimball model (FKM), which are two standard models of strongly correlated electrons, provide an interesting benchmark for the physics of locally correlated systems. We study the intermediate model, mass-imbalanced Hubbard model at half-filling on a 2D square lattice which connects continuously the HM to the FKM.We employ dynamical mean field theory (DMFT) and dynamical cluster approximation (DCA) using continuous-time auxiliary field method (CT-AUX) as self-consistent impurity solver to study the single particle spectral function and self-energy allowing us to map-out the phase diagram of the system. Solutions to the mass-imbalanced model cannot enforce paramagnetic self-consistency and therefore at low temperature result in paramagnetic (PM) to antiferromagnetic (AFM) transition. In addition, in the PM state and at finite temperature, we observed a spin dependent crossover from Fermi liquid (FL) regime to non-Fermi liquid (nFL) regime in which the FL regime is destroyed, monotonically, induced not only by the interaction but also by the mass imbalance. We present the results for small cluster DCA and explore its dependency on cluster size as well.The Hubbard model (HM) and the Falicov-Kimball model (FKM), which are two standard models of strongly correlated electrons, provide an interesting benchmark for the physics of locally correlated systems. We study the intermediate model, mass-imbalanced Hubbard model at half-filling on a 2D square lattice which connects continuously the HM to the FKM.We employ dynamical mean field theory (DMFT) and dynamical cluster approximation (DCA) using continuous-time auxiliary field method (CT-AUX) as self-consistent impurity solver to study the single particle spectral function and self-energy allowing us to map-out the phase diagram of the system. Solutions to the mass-imbalanced model cannot enforce paramagnetic self-consistency and therefore at low temperature result in paramagnetic (PM) to antiferromagnetic (AFM) transition. In addition, in the PM state and at finite temperature, we observed a spin dependent crossover from Fermi liquid (FL) regime to non-Fermi liquid (nFL) regime in which the FL regime is destroyed, monotonically, induced not only by the interaction but also by the mass imbalance. We present the results for small cluster DCA and explore its dependency on cluster size as well.

Jul 1, 20190 citations

The advent of ultracold alkaline-earth atoms in optical lattices has established a platform for investigating correlated quantum matter with SU(

N

) 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(

N

) 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(

N

) 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,

\left(\tfrac{1}{3}-δ,\tfrac{1}{3}+δ,\tfrac{1}{3}\right)

and

\left(\tfrac{1}{4}-δ,\tfrac{1}{4}+δ,\tfrac{1}{2}\right)

, with the flavor imbalance introduced as

δ

. 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(

N

) Fermi-Hubbard models but also inform future experimental search for new phases.

U/t

. We propose an experimental protocol to measure these correlation functions in cold atom experiments.