Mott insulators of ultracold fermionic alkaline earth atoms in three dimensions

Song, Hongwen; Hermele, Michael

doi:10.1103/physrevb.87.144423

Cited by 15 publications

(15 citation statements)

References 76 publications

(88 reference statements)

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“…In contrast to the well-studied SU(2) FHM, much less is known about the extended SU(N > 2)-symmetric case. Calculations are mostly limited to T = 0, low dimensions or approximated correlations, but point to very rich phase diagrams including novel magnetic and spin liquid phases [6][7][8][9][10][11][12][13][14]. Moreover, accurate predictions of thermodynamic quantities are even harder to obtain than for the SU(2) case, as most numerical algorithms fail for larger N due the unfavourable scaling of the Hilbert space.Fermionic 173 Yb has nuclear spin I = 5/2, but no electronic angular momentum in the ground state (J = 0).…”

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confidence: 99%

“…We determine the EoS for the density n(µ, T, N, U, t * ) over a wide arXiv:1511.07287v1 [cond-mat.quant-gas] 23 Nov 2015 range of parameters. In particular, we focus on the highest spin multiplicity of our system N = 6 and on the case N = 3, which was the subject of several theoretical studies [10][11][12][13][14]21]. By deriving the local compressibility directly from the measured EoS we are able to detect the emergence of the incompressible Mott phase.…”

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confidence: 99%

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Direct Probing of the Mott Crossover in theSU(N)Fermi-Hubbard Model

et al. 2016

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We report on a detailed experimental investigation of the equation of state (EoS) of the three-dimensional Fermi-Hubbard model (FHM) in its generalized SUðNÞ-symmetric form, using a degenerate ytterbium gas in an optical lattice. In its more common spin-1=2 form, the FHM is a central model of condensed-matter physics. The generalization to N > 2 was first used to describe multi-orbital materials and is expected to exhibit novel many-body phases in a complex phase diagram. By realizing and locally probing the SUðNÞ FHM with ultracold atoms, we obtain model-free access to thermodynamic quantities. The measurement of the EoS and the local compressibility allows us to characterize the crossover from a compressible metal to an incompressible Mott insulator. We reach specific entropies above Néel order but below that of uncorrelated spins. Having access to the EoS of such a system represents an important step towards probing predicted novel SUðNÞ phases. Strongly correlated fermionic many-body systems play a fundamental role in modern condensed-matter physics. A central model for these systems is the Fermi-Hubbard model (FHM), originally developed for describing interacting electrons in a crystal. It explains a wide range of observed phenomena such as metal-to-insulator transitions and magnetic order, and is believed to capture the essential physics of d-wave superfluidity in high-temperature superconductors [1,2]. The generalized SUðNÞ-symmetric version of the FHM was originally studied in the context of transition-metal oxides with effective higher spin [3].Although the FHM has been the object of a large number of studies in past decades, reaching a complete understanding has remained an elusive task, even for the spin-1=2 case. For strong repulsive interactions, the SU(2) FHM is known to give rise to a paramagnetic Mott insulator, where antiferromagnetic order emerges below the Néel temperature. Already in this limit of strong interactions and low temperature, the SUðN > 2Þ case has been predicted to exhibit a rich phase diagram with a variety of different correlated states [4][5][6][7][8][9][10][11][12][13].The development of experimental implementations of the three-dimensional (3D) FHM with ultracold atoms has provided a new approach for advancing our understanding of strongly correlated fermions in lattices [14]. The recent realization of degenerate gases of strontium and ytterbium [15,16], in combination with optical lattices, allows us to extend this beyond the conventional spin-1=2 FHM and to access the more general SUðN > 2Þ symmetry. Numerical calculations in this regime are, so far, mostly limited to T ¼ 0, low dimensions, or approximated correlations. Accurate predictions of thermodynamic quantities are even harder to obtain than for the SU(2) case, as most algorithms struggle with larger N due to the unfavorable scaling of the Hilbert space. Probing the thermodynamics of such systems, implemented with ultracold atoms, provides access to this challenging regime and allows for the testing of novel algorit...

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Direct Probing of the Mott Crossover in theSU(N)Fermi-Hubbard Model

et al. 2016

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“…The ground state physics of the spin Hamiltonian (2) has been explored for many values of N and lattice geometries over the last decades, see, e.g., Refs. [5,52,[78][79][80][81][82][83][84][85][86][89][90][91][92][93][94][95][96][97], and in most cases the structure of the ground states differs qualitatively from the Manhattan picture advocated in the previous section. Based on the current understanding, we expect only bipartite lattices with N = 2 to show a common sign structure of correlations from high to low temperatures.…”

Section: Disorder Temperatures and Lifshitz Transitionsmentioning

confidence: 70%

“…The original proposals and the subsequent experimental work motivated a broad range of theoretical and computational works on various aspects of SU(N ) quantum magnets . A significant effort was put into understanding the ground state (T = 0) phase diagrams of quantum spin models in the fundamental representation of SU(N ) [52,[78][79][80][81][82][83][84][85][86][87][88][89][90][91][92][93][94][95][96][97].…”

Section: Introductionmentioning

confidence: 99%

Structure of spin correlations in high-temperature SU(N) quantum magnets

Romen

Läuchli

2020

Phys. Rev. Research

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Quantum magnets with a large SU(N) symmetry are a promising playground for the discovery of new forms of exotic quantum matter. Motivated by recent experimental efforts to study SU(N) quantum magnetism in samples of ultracold fermionic alkaline-earth-like atoms in optical lattices, we study here the temperature dependence of spin correlations in the SU(N) Heisenberg spin model in a wide range of temperatures. We uncover a sizable regime in temperature, starting at T = ∞ down to intermediate temperatures and for all N 2, in which the correlations have a common spatial structure on a broad range of lattices, with the sign of the correlations alternating from one Manhattan shell to the next, while the amplitude of the correlations is rapidly decreasing with distance. Focussing on the one-dimensional chain and the two-dimensional square and triangular lattice for certain N, we discuss the appearance of a disorder and a Lifshitz temperature, separating the commensurate Manhattan high-T regime from a low-T incommensurate regime. We observe that this temperature window is associated to an approximately N-independent entropy reduction from the ln(N) entropy at infinite temperature. Our results are based on high-temperature series arguments and as well as large-scale numerical full diagonalization results of thermodynamic quantities for SU(3) and SU(4) square lattice samples, corresponding to a total Hilbert space of up to 4 × 10 9 states.

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“…the Hubbard model [2124] and its special-condition cases including the Heisenberg model [25,26], the Kugel-Khomskii model [27], and the Kondo model [28,29], and facilitates many experiments, like observing a chiral spin liquid [30], SU(N ) symmetry breaking states [31], and unconventional antiferromagnets [32].…”

Section: Introductionmentioning

confidence: 99%