Thermodynamics of strongly interacting fermions in two-dimensional optical lattices

Khatami, Ehsan; Rigol, Marcos

doi:10.1103/physreva.84.053611

Cited by 91 publications

(146 citation statements)

References 32 publications

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“…NLCEs use the same basis as hightemperature expansions, however, properties of clusters are calculated via exact diagonalisation, as opposed to a perturbative expansion in powers of the inverse temperature [8,33]. The site-based NLCE for the Hubbard model [34] is implemented here for a three-dimensional lattice and carried out to the eighth order for all thermodynamic quantities, except for S θ , where due to the reduced symmetry, only seven orders were obtained. Within its region of convergence (T /t 1.5 for any n and U ), NLCE results do not contain any systematic or statistical errors.…”

Section: Numerical Calculationsmentioning

confidence: 99%

Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms

Hart

Duarte

Yang

et al. 2015

Nature

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416

406

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Ultracold atoms in optical lattices have great potential to contribute to a better understanding of some of the most important issues in many-body physics, such as high-temperature (high-Tc) superconductivity [1]. Thirty years ago, Anderson suggested that the Hubbard model, a simplified representation of fermions moving on a periodic lattice, may contain the essence of copper oxide superconductivity [2]. The Hubbard model describes many of the features shared by the copper oxides, including an interaction-driven Mott insulating state and an antiferromagnetic (AFM) state. Optical lattices filled with a two-spin-component Fermi gas of ultracold atoms can faithfully realise the Hubbard model with readily tunable parameters, and thus provide a platform for the systematic exploration of its phase diagram [3,4]. Realisation of strongly correlated phases, however, has been hindered by the need to cool the atoms to temperatures as low as the magnetic exchange energy, and also by the lack of reliable thermometry [5]. Here we demonstrate spin-sensitive Bragg scattering of light to measure AFM spin correlations in a realisation of the three-dimensional (3D) Hubbard model at temperatures down to 1.4 times that of the AFM phase transition. This temperature regime is beyond the range of validity of a simple high-temperature series expansion, which brings our experiment close to the limit of the capabilities of current numerical techniques. We reach these low temperatures using a unique compensated optical lattice technique [6], in which the confinement of each lattice beam is compensated by a blue-detuned laser beam. The temperature of the atoms in the lattice is deduced by comparing the light scattering to determinantal quantum Monte Carlo [7] (DQMC) and numerical linked-cluster expansion [8] (NLCE) calculations. Further refinement of the compensated lattice may produce even lower temperatures which, along with light scattering thermometry, would open avenues for achieving and characterising other novel quantum states of matter, such as the pseudogap regime of the 2D Hubbard model.A two-spin-component Fermi gas in a simple cubic optical lattice may be described by a single-band Hubbard model with nearest-neighbour tunnelling t and on-site interaction U > 0. At a density n of one atom per site, and for sufficiently large U/t there is a crossover from a 'metallic' state to a Mott insulating regime [9] as the temperature T is reduced below U . The Mott regime has been demonstrated with ultracold atoms in an optical lattice by observing the reduction of doubly occupied sites [10] and the related reduction of the global compressibility [11]. For T below the Néel ordering temperature T N , which for U t is approximately equal to the exchange energy J = 4t 2 /U , the system undergoes a phase transition to an AFM state [12]. In the context of quantum simulations, AFM phases of Ising spins have been previously engineered with bosonic atoms in an optical lattice [13] and with spin-1 2 ions [14,15]. Also, nearest-neighbour AFM correlat...

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Section: Numerical Calculationsmentioning

confidence: 99%

Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms

Hart

Duarte

Yang

et al. 2015

Nature

Self Cite

416

406

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“…The effects of this interplay onto the double occupancy have been considered in previous theoretical studies in one dimension [42][43][44], two dimensions in the square [45][46][47] and hexagonal lattices [48], and three dimensions [43,[49][50][51][52], and experimentally in three dimensions [53,54].…”

Section: A Double Occupancymentioning

confidence: 99%

Competition of spin and charge excitations in the one-dimensional Hubbard model

et al. 2013

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Motivated by recent experiments with ultracold fermionic atoms in optical lattices, we study finite temperature magnetic correlations, as singlet and triplet correlations, and the double occupancy in the one-dimensional Hubbard model. We point out that for intermediate interaction strengths the double occupancy has an intriguing doubly nonmonotonic temperature dependence due to the competition between spin and charge modes, related to the Pomeranchuk effect. Furthermore, we determine properties of magnetic correlations in the temperature regimes relevant for current cold atom experiments and discuss effects of the trap on spatially integrated observables. We estimate the entropy and the temperature reached in the experiment by Greif, Uehlinger,

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“…It prevents from obtaining conclusive results for βt > 4 close to U/t = 8 and n = 0.875 within these approaches 35,36 . Alternatively, the model can be simulated directly in the thermodynamic limit using numerically linked cluster expansion (NLCE) 37 . This method gives well controlled results for small βt in the strongly correlated regime for the range of temperatures comparable with DQMC, but brakes down for larger βt 38 .…”

Section: Hubbard Modelmentioning

confidence: 99%

Variational tensor network renormalization in imaginary time: Benchmark results in the Hubbard model at finite temperature

2016

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A Gibbs operator e −βH for a 2D lattice system with a Hamiltonian H can be represented by a 3D tensor network, the third dimension being the imaginary time (inverse temperature) β. Coarsegraining the network along β results in an accurate 2D projected entangled-pair operator (PEPO) with a finite bond dimension. The coarse-graining is performed by a tree tensor network of isometries that are optimized variationally to maximize the accuracy of the PEPO. The algorithm is applied to the two-dimensional Hubbard model on an infinite square lattice. Benchmark results are obtained that are consistent with the best cluster dynamical mean-field theory and numerically linked cluster expansion in the regime of parameters where they yield mutually consistent results.

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Thermodynamics of strongly interacting fermions in two-dimensional optical lattices

Cited by 91 publications

References 32 publications

Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms

Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms

Competition of spin and charge excitations in the one-dimensional Hubbard model

Variational tensor network renormalization in imaginary time: Benchmark results in the Hubbard model at finite temperature

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