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arXiv:1607.08618 · Physical Review A

Ferromagnetic ground state of the SU(3) Hubbard model on the Lieb lattice

Wenxing Nie, Deping Zhang, Wei Zhang

Published Nov 10, 2017• 21 citations
arXivHTMLPDF

Abstract

We investigate the magnetic properties of a repulsive fermionic $\mathrm{SU}(3)$ Hubbard model on the Lieb lattice from weak to strong interaction by means of the mean-field approximation. To validate the method we employed, we first discuss the $\mathrm{SU}(2$) Hubbard model at the mean-field level, and find that our results are consistent with known rigorous theorems. We then extend the calculation to the case of $\mathrm{SU}(3)$ symmetry. We find that, at $4/9$ filling, the $\mathrm{SU}(3)$ symmetry spontaneously breaks into the $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ symmetry in the ground state, leading to a staggered ferromagnetic state for any repulsive $U$ at zero temperature. We then investigate the stability of the ferromagnetic state by relaxing the filling away from $4/9$, and conclude that the ferromagnetic state is sensitive but robust to fillings, as it can persist within a certain filling regime. We also apply the mean-field approximation to finite temperature to calculate the critical temperature and the critical entropy of the ferromagnetic state. As the resulting critical entropy per particle is significantly greater than what can be realized in experiments, we expect some quasi-long-range-ordered features of such a ferromagnetic state can be realized and observed with fermionic alkaline-earth-metal(-like) atoms loaded into optical lattices.

DOI
10.1103/physreva.96.053616

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We investigate the magnetic properties of a repulsive fermionic SU(3)\mathrm{SU}(3)SU(3) Hubbard model on the Lieb lattice from weak to strong interaction by means of the mean-field approximation. To validate the method we employed, we first discuss the SU(2\mathrm{SU}(2SU(2) Hubbard model at the mean-field level, and find that our results are consistent with known rigorous theorems. We then extend the calculation to the case of SU(3)\mathrm{SU}(3)SU(3) symmetry. We find that, at 4/94/94/9 filling, the SU(3)\mathrm{SU}(3)SU(3) symmetry spontaneously breaks into the SU(2)\ifmmode×\else\texttimes\fiU(1)\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)SU(2)\ifmmode×\else\texttimes\fiU(1) symmetry in the ground state, leading to a staggered ferromagnetic state for any repulsive UUU at zero temperature. We then investigate the stability of the ferromagnetic state by relaxing the filling away from 4/94/94/9, and conclude that the ferromagnetic state is sensitive but robust to fillings, as it can persist within a certain filling regime. We also apply the mean-field approximation to finite temperature to calculate the critical temperature and the critical entropy of the ferromagnetic state. As the resulting critical entropy per particle is significantly greater than what can be realized in experiments, we expect some quasi-long-range-ordered features of such a ferromagnetic state can be realized and observed with fermionic alkaline-earth-metal(-like) atoms loaded into optical lattices.
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.
We investigate an SU(3) Fermi-Hubbard model on a hypercubic lattice at finite temperatures, combining dynamical mean-field theory with continuous-time quantum Monte Carlo simulations. Taking strong correlations into account carefully, we find a ferromagnetically ordered state, in which one of the three components becomes dominant, when holes are doped away from one-third filling. Furthermore, we demonstrate that this ferromagnetically ordered phase undergoes a first-order transition to a paramagnetic state. We clarify the stability of the ferromagnetically ordered state against interaction strength, hole doping, and temperatures. The relevance of generalized Nagaoka ferromagnetism is also addressed, by comparing the results on the Bethe lattice.
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.
We study the SU(3) symmetric Fermi-Hubbard model (FHM) in the square lattice at 1/31/31/3-filling using numerically exact determinant quantum Monte Carlo and numerical linked-cluster expansion techniques. We present the different regimes of the model in the $T\text{\ensuremath{-}}U$ plane, which are characterized by local and short-range correlations, and capture signatures of the metal-insulator transition and magnetic crossovers. These signatures are detected as the temperature scales characterizing the rise of the compressibility, and an interaction-dependent change in the sign of the diagonal spin-spin correlation function. The analysis of the compressibility estimates the location of the metal-insulator quantum critical point at ${U}_{c}/t\ensuremath{\sim}6$, and provides a temperature scale for observing Mott physics at finite TTT. Furthermore, from the analysis of the spin-spin correlation function we observe that for $U/t\ensuremath{\gtrsim}6$ and $T\ensuremath{\sim}J=4{t}^{2}/U$ there is a development of a short-range two-sublattice (2SL) antiferromagnetic structure, as well as an emerging three-sublattice (3SL) antiferromagnetic structure as the temperature is lowered below $T/J\ensuremath{\lesssim}0.57$. This crossover from 2SL to 3SL magnetic ordering agrees with Heisenberg limit predictions, and has observable effects on the density of on-site pairs. Finally, we describe how the features of the regimes in the $T\ensuremath{-}U$ plane can be explored with alkaline-earth-like atoms in optical lattices with currently achieved experimental techniques and temperatures. The results discussed in this paper provide a starting point for the exploration of the SU(3) FHM upon doping.
We study Hubbard models for ultracold bosonic or fermionic atoms loaded into an optical lattice. The atoms carry a high spin F> 1/2, and interact on site via strong repulsive Van der Waals forces. Making convenient rearrangements of the interaction terms, and exploiting their symmetry properties, we derive low-energy effective models with nearest-neighbor interactions, and their properties. We apply our method to F =3/2, and 5/2 fermions on two-dimensional square lattice at quarter, and 1/6 fillings, respectively, and investigate mean-field equations for repulsive couplings. We find for F =3/2 fermions that the plaquette state appearing in the highly symmetric SU (4) case does not require fine tuning, and is stable in an extended region of the phase diagram. This phase competes with an SU (2) flux state, that is always suppressed for repulsive interactions in the absence of external magnetic field. The SU (2) flux state has, however, lower energy than the plaquette phase, and stabilizes in the presence of weak applied magnetic field. For F =5/2 fermions a similar SU (2) plaquette phase is found to be the ground state without external magnetic field.
SU(N)\mathrm{SU}(N)SU(N) symmetric fermions on a lattice, which can be realized in ultracold-atom-based quantum simulators, have very promising prospects for realizing exotic states of matter. Here we present the ground-state phase diagram of the repulsive SU(3) Hubbard model on a honeycomb lattice at 1/3 filling obtained from infinite projected entangled pair states tensor network calculations. In the strongly interacting limit the ground state has plaquette order. Upon decreasing the interaction strength U/tU/tU/t we find a first-order transition at U/t=7.2(2)U/t=7.2(2)U/t=7.2(2) into a dimerized, color-ordered state, which extends down to U/t=4.5(5)U/t=4.5(5)U/t=4.5(5), at which the Mott transition occurs and the ground state becomes uniform. Our results may serve as a prediction and benchmark for future quantum simulators of SU(3) fermions.