Observation of antiferromagnetic correlations in an ultracold SU($N$) Hubbard model

Taie, Shintaro; Ibarra-García-Padilla, Eduardo; Nishizawa, Naoki; Takasu, Yoshio; Kuno, Yoshihito; Wei, Haotian; Scalettar, Richard; Hazzard, Kaden R. A.; Takahashi, Yoshiro

doi:10.48550/arxiv.2010.07730

Cited by 19 publications

(33 citation statements)

References 36 publications

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“…As a result, AMO experiments can directly probe the role of SU(n) interactions * mika.perlin@gmail.com in controllable settings. Recent progress includes studies of the thermodynamic properties of SU(n) fermionic gases [20][21][22][23][24][25][26][27], SU(n) Hubbard phases and phase transitions [28][29][30], single- [31] and two-orbital [32][33][34][35] SU(n) magnetism, and multi-body SU(n)-symmetric interactions [36,37].…”

Section: Su(n) Symmetries Play An Important Role In Physicsmentioning

confidence: 99%

Engineering infinite-range SU($n$) interactions with spin-orbit-coupled fermions in an optical lattice

Perlin,

Barberena,

Mamaev

et al. 2021

Preprint

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We study multilevel fermions in an optical lattice described by the Hubbard model with on site SU(n)-symmetric interactions. We show that in an appropriate parameter regime this system can be mapped onto a spin model with all-to-all SU(n)-symmetric couplings. Raman pulses that address internal spin states modify the atomic dispersion relation and induce spin-orbit coupling, which can act as a synthetic inhomogeneous magnetic field that competes with the SU(n) exchange interactions. We investigate the mean-field dynamical phase diagram of the resulting model as a function of n and different initial configurations that are accessible with Raman pulses. Consistent with previous studies for n = 2, we find that for some initial states the spin model exhibits two distinct dynamical phases that obey simple scaling relations with n. Moreover, for n > 2 we find that dynamical behavior can be highly sensitive to initial intra-spin coherences. Our predictions are readily testable in current experiments with ultracold alkaline-earth(-like) atoms.

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Section: Su(n) Symmetries Play An Important Role In Physicsmentioning

confidence: 99%

Engineering infinite-range SU($n$) interactions with spin-orbit-coupled fermions in an optical lattice

Perlin,

Barberena,

Mamaev

et al. 2021

Preprint

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“…To calculate the thermodynamic observables, we employ two numerical techniques, DQMC [81,82] and NLCE [83,84], which have complementary strengths, and compare in some cases with low-order analytic HTSE and the non-interacting limit. The DQMC and NLCE are often the numerical methods of choice for the SU(2) FHM in the finite-temperature regime studied in ultracold matter [85][86][87][88][89], and we use our extensions of these methods to SU(N ) systems [67]. Generally speaking, the DQMC will perform best at weak to intermediate interactions, while the NLCE performs best at strong interactions; we present both methods where both are viable.…”

Section: A the Su(n ) Hubbard Hamiltonian And Observablesmentioning

confidence: 99%

“…, 10. In recent years, experiments with 173 Yb in OLs have probed the SU(N ) FHM's interesting physics: The Mott insulator state for SU (6) in three dimensions [64], the equation of state for SU (3) and SU (6) in three dimensions [65], nearest-neighbor antiferromagnetic (AFM) correlations in an SU(4) system with a dimerized OL [66], nearest-neighbor SU (6) AFM correlations in OLs with uniform tunneling matrix elements in one, two, and three dimensions [67], and recently a flavor-selective Mott insulator for SU (3) [68]. Furthermore, employing quantum gas microscopy [69][70][71][72][73][74][75] to discriminate finite temperature analogs of the variety of proposed ground states [30,31,[50][51][52][53][54][55] via direct observation of long-ranged correlations [67,[76][77][78] is expected to reveal a wealth of physics. All of these experimental efforts make an understanding of the 2D square lattice thermodynamics urgent.…”

Section: Introductionmentioning

confidence: 99%

Universal thermodynamics of an SU($N$) Fermi-Hubbard Model

Ibarra-García-Padilla,

Dasgupta,

Wei

et al. 2021

Preprint

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The SU(2) symmetric Fermi-Hubbard model (FHM) plays an essential role in strongly correlated fermionic many-body systems. In the one particle per site and strongly interacting limit U/t 1, it is effectively described by the Heisenberg Hamiltonian. In this limit, enlarging the spin and extending the typical SU(2) symmetry to SU(N ) has been predicted to give exotic phases of matter in the ground state, with a complicated dependence on N . This raises the question of what -if any -are the finite-temperature signatures of these phases, especially in the currently experimentally relevant regime near or above the superexchange energy. We explore this question for thermodynamic observables by numerically calculating the thermodynamics of the SU(N ) FHM in the two-dimensional square lattice near densities of one particle per site, using determinant Quantum Monte Carlo and Numerical Linked Cluster Expansion. Interestingly, we find that for temperatures above the superexchange energy, where the correlation length is short, the energy, number of on-site pairs, and kinetic energy are universal functions of N . Although the physics in the regime studied is well beyond what can be captured by low-order high-temperature series, we show that an analytic description of the scaling is possible in terms of only one-and two-site calculations.

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“…Another recent development is the study of cold-atom systems which offer a generalization of the well studied SU(2) Hubbard model with two spin species to the SU(N) Hubbard model with N species of Fermions [7][8][9][10]. Taking these Fermi Hubbard systems down to very low temperatures remains a challenge for experiments, but already interesting behavior can be seen at moderate to high temperatures.…”

Section: Introductionmentioning

confidence: 99%

Finite Temperature Strong Coupling Expansions for the SU(N) Hubbard Model

Singh,

Oitmaa

2022

Preprint

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We develop finite temperature strong coupling expansions for the SU(N) Hubbard Model in powers of βt, w = exp (−βU ) and 1 βU for arbitrary filling. The expansions are done in the grand canonical ensemble and are most useful at a density of one particle per site, where for U larger than or of order the Bandwidth, the expansions converge over a wide temperature range t 2 /U T 10U . By taking the limit w → 0, valid at temperatures much less than U , the expansions turn into a high temperature expansion for a dressed SU(N) Heisenberg model that includes nearest-neighbor exchange, further neighbor exchanges and ring exchanges known from the T = 0 perturbation theory of the SU(2) Hubbard model. Below a filling of one particle per site, the w → 0 limit corresponds to an effective t − J model. The onset of strong correlations can be identified by a plateau-like behavior in the entropy as a function of temperature. At small deviations from one particle per site, the expansions can be arranged in powers of a small parameter δ = 1 − n, the deviation from one particle per site, where the leading βt dependent terms correspond to holes sloshing around in a disordered SU(N) background. We use these expansions to calculate the thermodynamic properties of the model at moderate and high temperatures over a wide parameter range.

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Observation of antiferromagnetic correlations in an ultracold SU($N$) Hubbard model

Cited by 19 publications

References 36 publications

Engineering infinite-range SU($n$) interactions with spin-orbit-coupled fermions in an optical lattice

Engineering infinite-range SU($n$) interactions with spin-orbit-coupled fermions in an optical lattice

Universal thermodynamics of an SU($N$) Fermi-Hubbard Model

Finite Temperature Strong Coupling Expansions for the SU(N) Hubbard Model

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