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:1004.4650 · Physical Review A

Ferromagnetism of cold fermions loaded into a decorated square lattice

Kazuto Noda, Akihisa Koga, Norio Kawakami, Thomas Pruschke

Published Dec 11, 2009• 44 citations
arXivHTMLPDF

Abstract

We investigate two-component ultracold fermions loaded into a decorated square lattice, which are described by the Hubbard model with repulsive interactions and nearest-neighbor hoppings. By combining the real-space dynamical mean-field theory with the numerical renormalization-group method, we discuss how a ferromagnetically ordered ground state in the weak-coupling regime, which originates from the existence of a dispersionless band, is adiabatically connected to a Heisenberg ferrimagnetic state in the strong-coupling limit. The effects of level splitting and hopping imbalance are also addressed.

DOI
10.1103/physreva.80.063622

Related papers

Magnetically Ordered State of Cold Fermions on a Decorated Square Lattice

Kazuto Noda, Akihisa Koga, Norio Kawakami +1 more

We study two-component ultracold fermions with repulsive interactions, which are loaded into a decorated square lattice. By combining the real-space dynamical mean-field theory with the numerical renormalization group method, we discuss magnetic properties in the system. It is clarified how the ferromagnetically ordered ground state, which is stabilized by a flat band mechanism, is adiabatically connected to the ferrimagnetically ordered state expected in the strong coupling limit.

Journal of Low Temperature Physics•Oct 28, 2009•1 citation

Mott transition and antiferromagnetism of cold fermions in the decorated honeycomb lattice

Heng-Fu Lin, Yao‐Hua Chen, Haidi Liu +2 more

We investigate two-component ultracold fermions loaded in a decorated honeycomb lattice described by the Hubbard model with repulsive interactions and nearest-neighbor hopping. The phase transitions are studied by combining the cellular dynamical mean-field theory with the continuous-time quantum Monte Carlo method. For weak interactions, the quadratic band crossing point is broken to a linear band crossing point and the system becomes a semimetal. With increasing interaction, the system undergoes a first-order phase transition to an antiferromagnetic Mott insulator at low temperatures. Below the critical temperature, due to the charge nematic fluctuation, a nematic metal forms between the semimetal and the antiferromagnetic Mott insulator. The effects of lattice anisotropy are also addressed. Furthermore, we discuss how to detect these phases in real experiments.

Physical Review A•Nov 24, 2014•14 citations

Effective interactions between local hopping modulations on the square lattice

Huu T., Khagendra Adhikari, K. S. D. Beach

We address the problem of free fermions interacting with frozen gauge fields. In particular, we consider a tight-binding model of fermions on the square lattice in which (i) flux 0 or $π$ is threaded through each plaquette and (ii) each nearest-neighbor link is decorated with an Ising degree of freedom that describes the local modulation of the hopping amplitude. Following the standard Ruderman--Kittel--Kasuya--Yosida (RKKY) approach, we compute an effective spin model in the coupling strength order by order. Unlike the original RRKY result for site-centered SU(2) spins in which the leading contribution is an effective exchange term at the second-order, perturbation theory in link-centered Z$_2$ case produces a first-order term that favors a collective ferromagnetic moment. If, by some means, an antiferromagnetic configuration can be stabilized, the energetics of ground state is controlled by an effective Ising interaction acting pairwise at the long range across the system.

arXiv:1904.03220•Apr 5, 2019•0 citations

Exotic magnetic orders for high-spin ultracold fermions

E. Szirmai, Maciej Lewenstein

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.

arXiv:1009.4868•Europhysics Letters (EPL)•Mar 1, 2011•34 citations

Phase-separated ferromagnetism in a spin-imbalanced system of Fermi atoms loaded in an optical ladder: A density-matrix renormalization-group study

Masahiko Okumura, S. Yamada, Masahiko Machida +1 more

We consider repulsively interacting, cold fermionic atoms loaded on an optical ladder lattice in a trapping potential. The density-matrix renormalization-group method is used to numerically calculate the ground state for systematically varied values of interaction $U$ and spin imbalance $p$ in the Hubbard model on the ladder. The system exhibits rich structures, where a fully spin-polarized phase, spatially separated from other domains in the trapping potential, appears for large enough $U$ and $p$. The phase-separated ferromagnetism can be captured as a real-space image of the energy gap between the ferromagnetic and other states arising from the combined effect of the Nagaoka ferromagnetism extended to the ladder and the density dependence of the energy separation between competing states. We also predict how to maximize the ferromagnetic region.

arXiv:1008.3055•Physical Review A•Mar 9, 2011•16 citations

Two-Component Spin-Orbit Coupled Ultracold Atoms in the Weak and Strong Coupling Regimes

Even Thingstad

Motivated by recent experimental advances, we study two-component spin-orbit coupled ultracold bosonic atoms in two dimensions on a square optical lattice. Using a Bose-Hubbard model with spin-conserving and non-spin-conserving nearest neighbour hoppings and spin-dependent on-site density-density interaction, our goal is to characterize phase separation and spin structure in the weakly interacting and deep Mott regimes. \nFor the weakly coupled regime, we decouple interactions through a real space uniform density mean field theory. At zero temperature, this gives an analytic condition for the phase separation transition driven by inter- relative to intracomponent interaction. Solving the self-consistent equations at finite temperature reveals entropic remixing in the phase separated regime and a more surprising entropy driven phase separation in the mixed regime. This is a consequence of complex interplay between interaction and spin-orbit coupling, and can be explained through the effect of component imbalance on the effective single-particle dispersion relation. We also provide an alternate explanation based on thermal occupation of eigenstates with a characteristic imbalance.\nIn the strongly interacting Mott regime, we derive an effective spin Hamiltonian describing the magnetic phases of the Mott insulator. The competition between anisotropic {Heisenberg} and Dzyaloshinskii-Moriya interactions gives rise to various ferromagnetic, antiferromagnetic, spiral, stripe, vortex, and skyrmion phases. On basis of classical Monte-Carlo simulations in the literature, we reconstruct the phase diagram with a classical variational approach, while magnon excitation spectra and quantum fluctuations are calculated with Holstein-Primakoff transformation and subsequent spin wave expansion. The analysis shows that states with ferromagnetic or antiferromagnetic ordering of boson species are protected against thermal fluctuations by a gap, and well described by classical states. States with equal superposition of boson species at each lattice site are subject to relatively large quantum fluctuations, which may cause breakdown of the states within their classical parameter space regions. The dispersion relations are gapless and linear around the minima to lowest order in the spin wave expansion.

•Jan 1, 2017•0 citations
We investigate two-component ultracold fermions loaded into a decorated square lattice, which are described by the Hubbard model with repulsive interactions and nearest-neighbor hoppings. By combining the real-space dynamical mean-field theory with the numerical renormalization-group method, we discuss how a ferromagnetically ordered ground state in the weak-coupling regime, which originates from the existence of a dispersionless band, is adiabatically connected to a Heisenberg ferrimagnetic state in the strong-coupling limit. The effects of level splitting and hopping imbalance are also addressed.
We investigate two-component ultracold fermions loaded in a decorated honeycomb lattice described by the Hubbard model with repulsive interactions and nearest-neighbor hopping. The phase transitions are studied by combining the cellular dynamical mean-field theory with the continuous-time quantum Monte Carlo method. For weak interactions, the quadratic band crossing point is broken to a linear band crossing point and the system becomes a semimetal. With increasing interaction, the system undergoes a first-order phase transition to an antiferromagnetic Mott insulator at low temperatures. Below the critical temperature, due to the charge nematic fluctuation, a nematic metal forms between the semimetal and the antiferromagnetic Mott insulator. The effects of lattice anisotropy are also addressed. Furthermore, we discuss how to detect these phases in real experiments.
We address the problem of free fermions interacting with frozen gauge fields. In particular, we consider a tight-binding model of fermions on the square lattice in which (i) flux 0 or πππ is threaded through each plaquette and (ii) each nearest-neighbor link is decorated with an Ising degree of freedom that describes the local modulation of the hopping amplitude. Following the standard Ruderman--Kittel--Kasuya--Yosida (RKKY) approach, we compute an effective spin model in the coupling strength order by order. Unlike the original RRKY result for site-centered SU(2) spins in which the leading contribution is an effective exchange term at the second-order, perturbation theory in link-centered Z2_22​ case produces a first-order term that favors a collective ferromagnetic moment. If, by some means, an antiferromagnetic configuration can be stabilized, the energetics of ground state is controlled by an effective Ising interaction acting pairwise at the long range across the system.
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.
We consider repulsively interacting, cold fermionic atoms loaded on an optical ladder lattice in a trapping potential. The density-matrix renormalization-group method is used to numerically calculate the ground state for systematically varied values of interaction UUU and spin imbalance ppp in the Hubbard model on the ladder. The system exhibits rich structures, where a fully spin-polarized phase, spatially separated from other domains in the trapping potential, appears for large enough UUU and ppp. The phase-separated ferromagnetism can be captured as a real-space image of the energy gap between the ferromagnetic and other states arising from the combined effect of the Nagaoka ferromagnetism extended to the ladder and the density dependence of the energy separation between competing states. We also predict how to maximize the ferromagnetic region.
Motivated by recent experimental advances, we study two-component spin-orbit coupled ultracold bosonic atoms in two dimensions on a square optical lattice. Using a Bose-Hubbard model with spin-conserving and non-spin-conserving nearest neighbour hoppings and spin-dependent on-site density-density interaction, our goal is to characterize phase separation and spin structure in the weakly interacting and deep Mott regimes. \nFor the weakly coupled regime, we decouple interactions through a real space uniform density mean field theory. At zero temperature, this gives an analytic condition for the phase separation transition driven by inter- relative to intracomponent interaction. Solving the self-consistent equations at finite temperature reveals entropic remixing in the phase separated regime and a more surprising entropy driven phase separation in the mixed regime. This is a consequence of complex interplay between interaction and spin-orbit coupling, and can be explained through the effect of component imbalance on the effective single-particle dispersion relation. We also provide an alternate explanation based on thermal occupation of eigenstates with a characteristic imbalance.\nIn the strongly interacting Mott regime, we derive an effective spin Hamiltonian describing the magnetic phases of the Mott insulator. The competition between anisotropic {Heisenberg} and Dzyaloshinskii-Moriya interactions gives rise to various ferromagnetic, antiferromagnetic, spiral, stripe, vortex, and skyrmion phases. On basis of classical Monte-Carlo simulations in the literature, we reconstruct the phase diagram with a classical variational approach, while magnon excitation spectra and quantum fluctuations are calculated with Holstein-Primakoff transformation and subsequent spin wave expansion. The analysis shows that states with ferromagnetic or antiferromagnetic ordering of boson species are protected against thermal fluctuations by a gap, and well described by classical states. States with equal superposition of boson species at each lattice site are subject to relatively large quantum fluctuations, which may cause breakdown of the states within their classical parameter space regions. The dispersion relations are gapless and linear around the minima to lowest order in the spin wave expansion.