Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1202.4021 · Physical Review A

Monte Carlo study of fermionic trions in a square lattice with harmonic confinement

Steffen Backes, Irakli Titvinidze, A. Privitera, Walter Hofstetter

Published Jul 23, 2012• 3 citations
arXivHTMLPDF

Abstract

We investigate the strong-coupling limit of a three-component Fermi mixture in an optical lattice with attractive interactions. In this limit bound states (trions) of the three components are formed. We study the effective Hamiltonian for these composite fermions and show that it is asymptotically equivalent at the leading order to an antiferromagnetic Ising model. By using Monte Carlo simulations, we investigate the spatial arrangement of the trions in this regime and the formation of a trionic density wave, both in a homogeneous lattice and in the presence of an additional harmonic confinement. Depending on the strength of the confinement and on the temperature, we found several scenarios for the trionic distribution, including the coexistence of disordered trions with a density wave and band insulator phases. Our results show that, due to a proximity effect, staggered density modulations are induced in regions of the trap where they would not otherwise be present according to the local density approximation.

DOI
10.1103/physreva.86.013633

Related papers

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

Xiang Li, Yu Wang

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.

arXiv:2205.10225•Physical review. B./Physical review. B•Sep 3, 2024•2 citations

Crystallization of trions in SU(3) cold-atom gases trapped in optical lattices

Rafael A. Molina, J. Dukelsky, Peter Schmitteckert

Cold fermionic atoms with three different hyperfine states confined in optical lattices show pronounced atomic density waves (ADWs). These ADWs are pinned due to the confining potential that traps the atoms in the optical lattice and can be considered a crystal phase of strongly bound trions (CPT). We show that the crystalline phase is incompressible and robust against anisotropic interactions. We also show that it is generic in the presence of the trap due to its incompressibility. Numeric density matrix renormalization group calculations show evidence of a crossover between a trionic superfluid and the CPT state as a function of the strength of the interaction and as a function of the anisotropy of the interaction.

arXiv:0807.1886•Physical Review A•Jul 28, 2009•17 citations

Ising antiferromagnet with ultracold bosonic mixtures confined in a harmonic trap

Marco Guglielmino, Vittorio Penna, Barbara Capogrosso-Sansone

We present accurate results based on quantum Monte Carlo simulations of two-component bosonic systems on a square lattice and in the presence of an external harmonic confinement. Starting from hopping parameters and interaction strengths which stabilize the Ising antiferromagnetic phase in the homogeneous case and at half-integer filling factor, we study how the presence of the harmonic confinement challenges the realization of such a phase. We consider realistic trapping frequencies and number of particles, and we establish under which conditions, i.e., total number of particles and population imbalance, the antiferromagnetic phase can be observed in the trap.

arXiv:1105.5293•Physical Review A•Sep 20, 2011•15 citations

Trion ordering in the attractive three-color Hubbard model on a π -flux square lattice

Xiang Li, Yumeng Li, Quan Fu +1 more

Ultracold multicomponent fermions (atoms or molecules) loaded in optical lattices provide an ideal platform for simulating $\mathrm{SU}(N)$ 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.

arXiv:2512.06284•Physical Review A•Dec 3, 2025•0 citations

Ground-state properties of fermionic mixtures with mass imbalance in optical lattices

Pavol Farkašovský

Ground-state properties of fermionic mixtures confined in a one-dimensional optical lattice are studied numerically within the spinless Falicov-Kimball model with a harmonic trap. A number of remarkable results are found. i) At low particle filling the system exhibits phase separation with heavy atoms in the center of the trap and light atoms in the surrounding regions. ii) Insulating phases always coexist with metallic phases. iii) Atomic-density waves are observed in the insulating regions for all particle fillings near the half-filled lattice case. iv) The variance of the local density exhibits universal behavior (independent of the particle filling, the Coulomb interaction and the strength of a confining potential) over the whole region of the local density values.

arXiv:0805.4684•Europhysics Letters (EPL)•Oct 29, 2008•10 citations

Finite-temperature properties of attractive three-component fermionic atoms in optical lattices

Kensuke Inaba, Sei-ichiro Suga

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.

arXiv:0910.0648•Physical Review A•Oct 14, 2009•41 citations
We investigate the strong-coupling limit of a three-component Fermi mixture in an optical lattice with attractive interactions. In this limit bound states (trions) of the three components are formed. We study the effective Hamiltonian for these composite fermions and show that it is asymptotically equivalent at the leading order to an antiferromagnetic Ising model. By using Monte Carlo simulations, we investigate the spatial arrangement of the trions in this regime and the formation of a trionic density wave, both in a homogeneous lattice and in the presence of an additional harmonic confinement. Depending on the strength of the confinement and on the temperature, we found several scenarios for the trionic distribution, including the coexistence of disordered trions with a density wave and band insulator phases. Our results show that, due to a proximity effect, staggered density modulations are induced in regions of the trap where they would not otherwise be present according to the local density approximation.
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.
Cold fermionic atoms with three different hyperfine states confined in optical lattices show pronounced atomic density waves (ADWs). These ADWs are pinned due to the confining potential that traps the atoms in the optical lattice and can be considered a crystal phase of strongly bound trions (CPT). We show that the crystalline phase is incompressible and robust against anisotropic interactions. We also show that it is generic in the presence of the trap due to its incompressibility. Numeric density matrix renormalization group calculations show evidence of a crossover between a trionic superfluid and the CPT state as a function of the strength of the interaction and as a function of the anisotropy of the interaction.
We present accurate results based on quantum Monte Carlo simulations of two-component bosonic systems on a square lattice and in the presence of an external harmonic confinement. Starting from hopping parameters and interaction strengths which stabilize the Ising antiferromagnetic phase in the homogeneous case and at half-integer filling factor, we study how the presence of the harmonic confinement challenges the realization of such a phase. We consider realistic trapping frequencies and number of particles, and we establish under which conditions, i.e., total number of particles and population imbalance, the antiferromagnetic phase can be observed in the trap.
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.
Ground-state properties of fermionic mixtures confined in a one-dimensional optical lattice are studied numerically within the spinless Falicov-Kimball model with a harmonic trap. A number of remarkable results are found. i) At low particle filling the system exhibits phase separation with heavy atoms in the center of the trap and light atoms in the surrounding regions. ii) Insulating phases always coexist with metallic phases. iii) Atomic-density waves are observed in the insulating regions for all particle fillings near the half-filled lattice case. iv) The variance of the local density exhibits universal behavior (independent of the particle filling, the Coulomb interaction and the strength of a confining potential) over the whole region of the local density values.
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.