Quantum Monte Carlo study of the two-dimensional fermion Hubbard model

Varney, Christopher; Lee, C.-R.; Bai, Zhaojun; Chiesa, Simone; Jarrell, Mark; Scalettar, Richard

doi:10.1103/physrevb.80.075116

Cited by 151 publications

(151 citation statements)

References 45 publications

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“…For U/t = 2, it appears advantageous to use the DCA-DMET formulation already for clusters of size L c 4, while at U/t = 4,6 it appears necessary to go to clusters larger than the largest linear size used in this study, L c = 10. [27], pinning field QMC simulations by Wu and coworkers [28], AFQMC with TABC by Qin et al [18] and the modified boundary conditions by Sorella [17].…”

Section: B 2d Hubbard Modelmentioning

confidence: 99%

Cluster size convergence of the density matrix embedding theory and its dynamical cluster formulation: A study with an auxiliary-field quantum Monte Carlo solver

et al. 2017

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We investigate the cluster size convergence of the energy and observables using two forms of density matrix embedding theory (DMET): the original cluster form (CDMET) and a new formulation motivated by the dynamical cluster approximation (DCA-DMET). Both methods are applied to the half-filled one-and two-dimensional Hubbard models using a sign-problem free auxiliary-field quantum Monte Carlo impurity solver, which allows for the treatment of large impurity clusters of up to 100 sites. While CDMET is more accurate at smaller impurity cluster sizes, DCA-DMET exhibits faster asymptotic convergence towards the thermodynamic limit. We use our two formulations to produce new accurate estimates for the energy and local moment of the two-dimensional Hubbard model for U/t = 2,4,6. These results compare favorably with the best data available in the literature, and help resolve earlier uncertainties in the moment for U/t = 2.

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Section: B 2d Hubbard Modelmentioning

confidence: 99%

Cluster size convergence of the density matrix embedding theory and its dynamical cluster formulation: A study with an auxiliary-field quantum Monte Carlo solver

et al. 2017

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“…Rigorous, near-exact results are available in certain limits [6]: at high temperatures from series expansions [7][8][9][10], in infinite dimensions from converged dynamical mean-field theory [11][12][13][14], and at weak coupling from perturbation theory [15] and renormalization group analysis [16,17]. Further, at half filling, the model has no fermion sign problem, and unbiased determinantal quantum Monte Carlo simulations can be converged [18]. Away from these limits, however, approximations are necessary.…”

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confidence: 99%

Ground-state phase diagram of the square lattice Hubbard model from density matrix embedding theory

2016

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We compute the ground-state phase diagram of the Hubbard and frustrated Hubbard models on the square lattice with density matrix embedding theory using clusters of up to 16 sites. We provide an error model to estimate the reliability of the computations and complexity of the physics at different points in the diagram. We find superconductivity in the ground state as well as competition between inhomogeneous charge, spin, and pairing states at low doping. The estimated errors in the study are below T c in the cuprates and on the scale of contributions in real materials that are neglected in the Hubbard model. DOI: 10.1103/PhysRevB.93.035126 The Hubbard model [1][2][3] is one of the simplest quantum lattice models of correlated electron materials. Its one-band realization on the square lattice plays a central role in understanding the essential physics of high-temperature superconductivity [4,5]. Rigorous, near-exact results are available in certain limits [6]: at high temperatures from series expansions [7][8][9][10], in infinite dimensions from converged dynamical mean-field theory [11][12][13][14], and at weak coupling from perturbation theory [15] and renormalization group analysis [16,17]. Further, at half filling, the model has no fermion sign problem, and unbiased determinantal quantum Monte Carlo simulations can be converged [18]. Away from these limits, however, approximations are necessary. Many numerical methods have been applied to the model at both finite and zero temperatures, including fixed-node, constrained path, determinantal, and variational quantum Monte Carlo (QMC) [19][20][21][22][23][24][25][26][27][28][29], density matrix renormalization group (DMRG) [30][31][32], dynamical cluster (DCA) [33,34], (cluster) dynamical mean-field theories (CDMFT) [35,36], and variational cluster approximations (VCA) [37,38]. (We refer to DCA/CDMFT/VCA collectively as Green's function cluster theories.) These pioneering works have suggested rich phenomenology in the phase diagram including metallic, antiferromagnetic, and d-wave (and other kinds of) superconducting phases, a pseudogap regime, inhomogeneous orders such as stripes, and charge, spin, and pairdensity waves, as well as phase separation [6,19,20,24,25,[27][28][29]32,35,[39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58]. However, as different numerical methods have yielded different pictures of the ground-state phase diagram, a precise quantitative picture of the ground-state phase diagram has yet to emerge.It is the goal of this paper to produce such a quantitative picture as best as possible across the full Hubbard model phase diagram below U = 8. Our method of choice is density matrix embedding theory (DMET), which is very accurate in this regime [59][60][61][62][63][64][65][66], employed together with clusters of up to 16 sites and thermodynamic extrapolation. We carefully calibrate errors in our calculations, giving error bars to quantify the remaining uncertainty in our phase diagram. These error bars also serve,...

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“…Some of the issues are similar to the repulsive case, in particular the coexistence of phases as the density varies across the trap. 18 However, the attractive case has several important distinctions, specifically the existence of known finite-temperature phase transitions in two dimensions. In addition, in the repulsive case there is a broad range of chemical potentials µ which fall within the "Mott gap" and for which the fermion density ρ = 1.…”

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confidence: 99%

Superconductivity and charge order of confined Fermi systems

et al. 2012

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The low-temperature properties of the two-dimensional attractive Hubbard model are strongly influenced by the fermion density. Away from half-filling, there is a finite-temperature transition to a phase with s-wave pairing order. However, Tc is suppressed to zero at half-filling, where long-range charge-density-wave order also appears, degenerate with superconductivity. This paper presents Determinant Quantum Monte Carlo simulations of the attractive Hubbard model in the presence of a confining potential Vtrap which makes the fermion density ρ inhomogeneous across the lattice. Pair correlations are shown to be large at low temperatures in regions of the trapped system with incommensurate filling, and to exhibit a minimum as the local density ρ(i) passes through one fermion per site. In this ring of ρ(i) = 1, charge order is enhanced. A comparison is made between treating Vtrap within the local-density approximation (LDA) and in an ab initio manner. It is argued that certain sharp features of the LDA result at integer filling do not survive the proximity of doped sites. The critical temperature of confined systems of fixed characteristic density is estimated.

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Quantum Monte Carlo study of the two-dimensional fermion Hubbard model

Cited by 151 publications

References 45 publications

Cluster size convergence of the density matrix embedding theory and its dynamical cluster formulation: A study with an auxiliary-field quantum Monte Carlo solver

Cluster size convergence of the density matrix embedding theory and its dynamical cluster formulation: A study with an auxiliary-field quantum Monte Carlo solver

Ground-state phase diagram of the square lattice Hubbard model from density matrix embedding theory

Superconductivity and charge order of confined Fermi systems

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