Critical temperature for the two-dimensional attractive Hubbard model

Paiva, Thereza; Santos, Raimundo R. dos; Scalettar, Richard; Denteneer, P. J. H.

doi:10.1103/physrevb.69.184501

Cited by 114 publications

(120 citation statements)

References 33 publications

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“…We find the BKT transition temperature in the Lieb lattice to be k B T c;BKT ¼ πℏ 2 D s ðT c;BKT Þ=8 ¼ 0.133 J [45] at the optimal coupling U ≈ 4 J [ Fig. 4(a)], to be compared with the quantum Monte Carlo estimate k B T c;BKT ∼ 0.10-0.13 J at U ¼ 4 J for the 2D simple square lattice [66] (for three dimensions see Ref. [67]).…”

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confidence: 99%

Geometric Origin of Superfluidity in the Lieb-Lattice Flat Band

et al. 2016

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The ground state and transport properties of the Lieb lattice flat band in the presence of an attractive Hubbard interaction are considered. It is shown that the superfluid weight can be large even for an isolated and strictly flat band. Moreover the superfluid weight is proportional to the interaction strength and to the quantum metric, a band structure quantity derived solely from the flat-band Bloch functions. These predictions are amenable to verification with ultracold gases and may explain the anomalous behaviour of the superfluid weight of high-Tc superconductors.

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Geometric Origin of Superfluidity in the Lieb-Lattice Flat Band

et al. 2016

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“…At lower temperatures, T ≈ J/4 = t 2 /U , there is a second peak associated with magnetic ordering (pair coherence). Interestingly, in two dimensions, this two peak structure appears to survive even down to weak coupling where the two energy scales merge, [28] in contrast to the behavior in one dimension, [36,37,38,39,40] and in the paramagnetic phase in infinite dimensions. [41,42,43] What happens to this behavior when disorder is introduced, specifically when U = 0 sites are inserted, as in …”

Section: Specific Heatmentioning

confidence: 94%

“…T c decreases gradually thereafter. [26,27] There is some debate as to the exact value of the maximal T c , with estimates [28] in the range 0.05t < T c,max < 0.2t. The problem lies with the rather large system sizes needed to study Kosterlitz-Thouless transitions numerically, and hence to benchmark the accuracy of the approximate analytic calculations.…”

Section: The Model and Computational Approachmentioning

confidence: 99%

Destruction of superconductivity by impurities in the attractive Hubbard model

et al. 2005

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We study the effect of U = 0 impurities on the superconducting and thermodynamic properties of the attractive Hubbard model on a square lattice. Removal of the interaction on a critical fraction of fcrit ≈ 0.30 of the sites results in the destruction of off-diagonal long range order in the ground state. This critical fraction is roughly independent of filling in the range 0.75 < ρ < 1.00, although our data suggest that fcrit might be somewhat larger below half-filling than at ρ = 1. We also find that the two peak structure in the specific heat is present at f both below and above the value which destroys long range pairing order. It is expected that the high T peak associated with local pair formation should be robust, but apparently local pairing fluctuations are sufficient to generate a low temperature peak. PACS numbers:The study of the interplay of disorder and interactions is one of the central problems in condensed matter physics, and has been analyzed through a wide range of techniques. [1,2,3,4,5,6,7] Quantum Monte Carlo (QMC) is one approach which has been applied only relatively recently, but now a number of investigations of the disordered, repulsive Hubbard model exist, both on finite lattices [8,9,10] and within dynamical mean field theory where the momentum dependence of the selfenergy is neglected.[11] Several interesting effects, including the possibility of the enhancement of T Neel by site disorder [11], the occurrence of a Mott transition away from half-filling, [12] and a change in the temperature dependence of the resistivity from insulating to metallic behavior when interactions are turned on, [13] have been observed. These studies have also explored different types of disorder, including randomness in the chemical potential, hopping, Zeeman fields, and on-site interaction. [14] At half-filling, some of these disorder types preserve particle-hole symmetry which has an important effect both on the behavior of the static (magnetic and charge) correlations, [8] and on the conductivity.[15]The work described above concerns the interplay of randomness and repulsive interactions. Superconductorinsulator transitions provide a motivation to explore models with an effective attractive electron-electron interaction, since these novel transitions are widely studied experimentally, especially in two dimensions. [16,17,18,19] However, QMC studies of models like the attractive Hubbard Hamiltonian with disorder are less numerous than for the repulsive case. [13,20] Previous work focused on locating the critical site disorder strength for the insulating transition and determining the value of the conductivity and its possible universality, [21] and on the interplay between the loss of phase coherence and the closing of the gap in the density of states. [22,23] Another particularly interesting application of the attractive Hubbard model with disorder is the question of how inhomogeneities and pairing affect each other in high-temperature superconductors. The attractive Hubbard model is the simplest Hamilton...

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“…A particularly powerful method of exploring finitetemperature properties is the hybridization-expansion CTQMC method, 26,27) which enables us to study the attractive Hubbard model in both the weak-and strongcoupling regimes. 28) In the study, by varying the ratio of the bandwidths r ¼ D # =D " at a fixed D " ¼ 1 (energy unit), we proceed to discuss how mass imbalance affects lowtemperature properties.In a mass balanced system (r ¼ 1), low-energy properties have been studied in one dimension, [29][30][31][32] two dimensions, 33,34) and infinite dimensions. [35][36][37][38][39][40][41] It is known that the DW and SF states are degenerate on a bipartite lattice in two and higher dimensions at half filling.…”

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“…In a mass balanced system (r ¼ 1), low-energy properties have been studied in one dimension, [29][30][31][32] two dimensions, 33,34) and infinite dimensions. [35][36][37][38][39][40][41] It is known that the DW and SF states are degenerate on a bipartite lattice in two and higher dimensions at half filling.…”

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Low-Temperature Properties of the Fermionic Mixtures with Mass Imbalance in Optical Lattice

Takemori

Koga

2012

J. Phys. Soc. Jpn.

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We study the attractive Hubbard model with mass imbalance to clarify the low-temperature properties of fermionic mixtures in an optical lattice. By combining dynamical mean-field theory with continuous-time quantum Monte Carlo simulation, we discuss the competition between the superfluid and density wave states at half filling. By calculating the energy and order parameter for each state, we clarify that the coexisting (supersolid) state, where the density wave and superfluid states are degenerate, is realized in the system. We then determine the phase diagram at finite temperatures.KEYWORDS: superfluid, density wave, mass-imbalanced system, continuous-time Monte Carlo simulationThe superfluid state in ultracold fermionic systems has attracted considerable interest since the successful realization of the Bose-Einstein condensation in 6 Li 2 molecules. 1,2) Owing to the high controllability of the system, remarkable phenomena have been observed such as the BCS-BEC crossover 3,4) and the superfluid state in a spin-imbalanced system, 5,6) where Cooper pairs are composed of ions with distinct hyperfine states. Recently, fermionic mixtures with distinct ions, e.g., 6 Li and 40 K, have experimentally been realized, 7,8) which stimulates further theoretical investigations on superfluid states in a mass-imbalanced system. [9][10][11][12][13][14][15][16][17] One of the interesting questions in such a massimbalanced system is how the superfluid state is realized when the lattice potential is loaded, so called an optical lattice. 18) In the lattice system, 19) the density wave (DW) state is naively expected, in addition to the SF state, since less mobile fermions tend to crystallize in the lattice, particularly, at half filling. It is desired to systematically discuss how the SF state competes or coexists with the DW state in an optical lattice system. This topic is closely related to an important issue in condensed matter physics, so called the supersolid state, [20][21][22][23][24] since the DW state can be regarded as a type of solid state. Therefore, an optical lattice system with mass imbalance should provide an ideal stage for studies of supersolid state in fermionic systems.Motivated by this, we study the low-temperature properties of a fermionic mixture in an optical lattice, combining dynamical mean-field theory (DMFT) 25) with continuoustime quantum Monte Carlo (CTQMC) simulation. 26,27) By calculating the order parameters for the DW and SF states, we determine the phase diagram at finite temperatures and clarify how the coexisting state is stabilized against the mass imbalance.In this paper, we consider the following attractive Hubbard model with different masses 19) aswhere hi; ji denotes the nearest neighbor site, c y i ðc i Þ is the creation (annihilation) operator of a fermion at the ith site with spin ð¼ "; #Þ and n i ¼ c y i c i . U ð> 0Þ is the attractive interaction and t is the hopping amplitude for the fermion with spin , where the effect of the mass imbalance is taken into account.We examine the low-t...

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Critical temperature for the two-dimensional attractive Hubbard model

Cited by 114 publications

References 33 publications

Geometric Origin of Superfluidity in the Lieb-Lattice Flat Band

Geometric Origin of Superfluidity in the Lieb-Lattice Flat Band

Destruction of superconductivity by impurities in the attractive Hubbard model

Low-Temperature Properties of the Fermionic Mixtures with Mass Imbalance in Optical Lattice

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