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arXiv:2205.10225 · Physical review. B./Physical review. B

Coexisting Néel and charge density wave orders in attractive three-color fermions

Xiang Li, Yu Wang

Published Sep 3, 2024• 2 citations
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Abstract

In optical lattices attractive ultracold fermions with three hyperfine-spin components (colors) can form three fermionic configurations depending on the interactions---unbound fermions, on-site trions, and off-site trions---leading to the coexistence of multiple fermionic species in the ordered phase, which demonstrates that the attractive three-color fermions are unique from other correlated fermion systems and may host intriguing phases and phase transitions. At temperatures below the superexchange energy scale, we employ the determinant quantum Monte Carlo (QMC) method to investigate the phases and phase transitions in the half-filled attractive three-color Hubbard model on a honeycomb lattice where the Hubbard interactions are color dependent (anisotropic interactions) and the coupling between color 3 and colors (1, 2) serves as a control parameter. In the coupling regime where on-site and off-site trions coexist, our QMC simulations demonstrate coexisting N\'eel and charge density wave (CDW) orders which are common in condensed matter but rare in ultracold atoms. At weak coupling where the color superfluid (CSF) order is scattered by color-3 fermions, we find that very small coupling of color 3 with colors (1, 2) can destroy the CSF order and that the vanishing of the CSF order is not immediately accompanied by the emergence of the on-site trionic phase, which strikingly disagrees with the prevalent results of dynamical mean-field theory. The underlying mechanisms of the coexisting N\'eel/CDW orders and of the CSF order breaking are also presented based on intuitive physical pictures.

DOI
10.1103/physrevb.110.115105

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In optical lattices attractive ultracold fermions with three hyperfine-spin components (colors) can form three fermionic configurations depending on the interactions---unbound fermions, on-site trions, and off-site trions---leading to the coexistence of multiple fermionic species in the ordered phase, which demonstrates that the attractive three-color fermions are unique from other correlated fermion systems and may host intriguing phases and phase transitions. At temperatures below the superexchange energy scale, we employ the determinant quantum Monte Carlo (QMC) method to investigate the phases and phase transitions in the half-filled attractive three-color Hubbard model on a honeycomb lattice where the Hubbard interactions are color dependent (anisotropic interactions) and the coupling between color 3 and colors (1, 2) serves as a control parameter. In the coupling regime where on-site and off-site trions coexist, our QMC simulations demonstrate coexisting N'eel and charge density wave (CDW) orders which are common in condensed matter but rare in ultracold atoms. At weak coupling where the color superfluid (CSF) order is scattered by color-3 fermions, we find that very small coupling of color 3 with colors (1, 2) can destroy the CSF order and that the vanishing of the CSF order is not immediately accompanied by the emergence of the on-site trionic phase, which strikingly disagrees with the prevalent results of dynamical mean-field theory. The underlying mechanisms of the coexisting N'eel/CDW orders and of the CSF order breaking are also presented based on intuitive physical pictures.
Ultracold multicomponent fermions (atoms or molecules) loaded in optical lattices provide an ideal platform for simulating SU(N)\mathrm{SU}(N)SU(N) Hubbard models that host unconventional many-body quantum states beyond SU(2). A prime example is the attractive three-color Hubbard model, in which trion states emerge at strong coupling. Nevertheless, much of its trion ordering on two-dimensional lattices remains uncertain. Here, we employ the determinant quantum Monte Carlo method to simulate the attractive three-color Hubbard model on a $\ensuremath{\pi}$-flux square lattice at half filling. We show that color-dependent attractive interaction can induce the coexisting charge density wave (CDW) and N\'eel-ordered states in the three-color $\ensuremath{\pi}$-flux Hubbard model. In particular, enhanced charge fluctuations (cf. honeycomb lattice) cause much stronger N\'eel ordering on the $\ensuremath{\pi}$-flux square lattice. The coexisting charge and N\'eel orders survive up to a melting temperature, at which they vanish simultaneously. The Ginzburg-Landau (GL) analysis on the coexistence of CDW and N\'eel orders demonstrates how color-dependent Hubbard interactions stabilize coexisting orders from the perspective of GL free energy principle.
The recent experimental realization of the half-filled three-color Fermi-Hubbard model on a square optical lattice provides a novel platform for exploring exotic states of matter beyond conventional SU(2) systems. In this Letter, we investigate the three-color Fermi-Hubbard model with color-dependent attractive interactions using determinant quantum Monte Carlo simulations. We find that, at quantum degenerate temperatures, a lattice Fermi supersolid state emerges from the interplay between a moderately-to-strongly interacting two-color subsystem and a weakly coupled third-color environment. This supersolid state, characterized by the coexistence of charge-density-wave and color-superfluid orders, is highly promising for experimental detection with current techniques. Our results demonstrate that the attractive three-color Fermi-Hubbard model on a square optical lattice offers an experimentally accessible system for exploring the supersolidity of ultracold lattice fermions, requiring only a simple lattice geometry and easily tunable onsite interactions.
We investigate three-component (colors) fermionic atoms with anisotropic attractive interactions in optical lattices at half filling using the dynamical mean field theory. In the weakly interacting region the color superfluid (CSF) state emerges, where atoms with two of three colors form the Cooper pairs. As the interaction is increased, a first-order quantum phase transition to the trionic state occurs, where singlet bound states of three different color atoms are formed. We show that the trionic state survives up to a fairly large anisotropic region. The phase diagram for the CSF and trionic states is obtained.
We perform the projector quantum Monte Carlo simulation of the half-filled attractive SU(3) Hubbard model on a honeycomb lattice, exploring the effects of SU(3) symmetry on the correlated attractive Dirac fermions. Our simulation indicates the absence of pairing order in the system and shows a quantum phase transition from the semimetal to charge density wave (CDW) at the critical point Uc=−1.52(2)U_c=-1.52(2)Uc​=−1.52(2). We demonstrate that this quantum phase transition belongs to the chiral Ising universality class according to the numerically determined critical exponents ν=0.82(3)\nu=0.82(3)ν=0.82(3) and η=0.58(4)\eta=0.58(4)η=0.58(4). With the increase of coupling strength, the trion formation is investigated, and the change in probability of the on-site trion occupancy infers the coexistence of on-site trionic and off-site trionic CDW states at half-filling.
We perform the projector quantum Monte Carlo (QMC) simulation to study the trion formation and quantum phase transition in the half filled attractive SU(3) Hubbard model on a honeycomb lattice. With increasing attractive Hubbard interaction, our simulations demonstrate a continuous quantum phase transition from the semimetal to charge-density wave (CDW) at the critical coupling ${U}_{c}/t=\ensuremath{-}1.52(2)$. The critical exponents $\ensuremath{\nu}=0.82(3)$ and $\ensuremath{\eta}=0.58(4)$ determined by the QMC simulation remarkably disagree with those of the N=3N=3N=3 chiral Ising universality class suggested by the effective Gross-Neveu-Yukawa (GNY) theory, but coincide with the N=1N=1N=1 chiral Ising universality class. In the CDW phase, we show that on-site and off-site trions coexist and the off-site trion forms a local bond state. Our work not only illustrates the formation of off-site trions in two-dimensional Hubbard model but also raises doubts about the extent of applicability of GNY model on attractive SU(3) Dirac fermions.
We investigate the finite-temperature properties of attractive three-component (colors) fermionic atoms in optical lattices using a self-energy functional approach. As the strength of the attractive interaction increases in the low-temperature region, we observe a second-order transition from a Fermi liquid to a color superfluid (CSF), where atoms from two of the three colors form Cooper pairs. In the strong attractive region, we observe a first-order transition from a CSF to a trionic state, where three atoms with different colors form singlet bound states. A crossover between a Fermi liquid and a trionic state is observed in the high-temperature region. We present a phase diagram covering zero to finite temperatures. We demonstrate that the CSF transition temperature is enhanced by the anisotropy of the attractive interaction.