Numerical study of the two-dimensional Hubbard model

White, Steven R.; Scalapino, D. J.; Sugar, R.; Loh, Eugene; Gubernatis, J. E.; Scalettar, Richard

doi:10.1103/physrevb.40.506

Cited by 926 publications

(797 citation statements)

References 14 publications

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“…Consequently, the determinant division det L(I+A)R det LR and the matrix inverse (L(I + A)R) −1 can be calculated using a fast updating algorithm. 27,28 We find that the matrix form of e λγf iσ = e λγ(d † i,x,σ d i,y,σ +h.c.) can be cast into a similar form as Eq.…”

Section: Model and Numerical Approachmentioning

confidence: 99%

Magnetic and pairing properties of a two-orbital model for the pnictide superconductors: a quantum Monte Carlo study

Liu

Huang

Wang

2014

J. Phys.: Condens. Matter

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Using the constrained-path Monte Carlo method, a two-orbital model for the pnictide superconductors is studied at half filling and in both the electron-and hole-doped cases. At half filling, a stable (π, 0)/(0, π) magnetic order is explicitly observed, and the system tends to be in an orthomagnetic order rather than the striped antiferromagnetic order when increasing the Coulomb repulsion U . In the electron-doped case, the (π, 0)/(0, π) magnetic order is enhanced upon doping and suppressed eventually, and a s± pairing state dominates all the possible nearest-neighbor-bond pairings. Whereas in the hole-doped case, the magnetic order is straightforwardly suppressed and two nearly degenerate A1g and B1g intraband pairings become the dominant ones.

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Section: Model and Numerical Approachmentioning

confidence: 99%

Magnetic and pairing properties of a two-orbital model for the pnictide superconductors: a quantum Monte Carlo study

Liu

Huang

Wang

2014

J. Phys.: Condens. Matter

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“…This is consistent with the existence of long-range antiferromagnetic order only at x = 0, m = 0, T = 0, and U/4t > 0, in agreement with the numerical results of Refs. 51,52 , and its replacement by a short-range spin order both for (i) x = 0, T > 0, and U/4t > 0 and (ii) 0 < x ≪ 1, T ≥ 0, and U/4t > 0.…”

Section: The C Momentum Band and C Fermion Energy Dispersionmentioning

confidence: 99%

The square-lattice quantum liquid of charge c fermions and spin-neutral two-spinon s1 fermions

Carmelo

2010

Nuclear Physics B

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The momentum bands, energy dispersions, and velocities of the charge c fermions and spin-neutral two-spinon s1 fermions of a square-lattice quantum liquid referring to the Hubbard model on such a lattice of edge length L in the one-and two-electron subspace are studied. The model involves the effective nearest-neighbor integral t and on-site repulsion U and can be experimentally realized in systems of correlated ultra-cold fermionic atoms on an optical lattice and thus our results are of interest for such systems. Our investigations profit from a general rotated-electron description, which is consistent with the model global SO(3)×SO(3)×U (1) symmetry. For the model in the oneand two-electron subspace the discrete momentum values of the c and s1 fermions are good quantum numbers so that in contrast to the original strongly-correlated electronic problem their interactions are residual. The use of our description renders an involved many-electron problem into a quantum liquid with some similarities with a Fermi liquid. For the Hubbard model on a square lattice in the one-and two-electron subspace a composite s1 fermion consists of a spin-singlet spinon pair plus an infinitely thin flux tube attached to it. In the U/4t → ∞ limit of infinite on-site interaction the c fermions become non-interacting spinless fermions and the s1 fermion occupancy configurations that generate the spin degrees of freedom of spin-density m = 0 ground states become within a suitable mean-field approximation for the fictitious magnetic field Bs1 ex 3 brought about by the correlations of the original N electron problem those of a full lowest Landau level with N/2 degenerate one-s1 fermion states of the two-dimensional quantum Hall effect. In turn, for U/4t finite the degeneracy of the N/2 one-s1-fermion states is removed by the emergence of a finite-energy-bandwidth s1 fermion dispersion yet the number of s1 band discrete momentum values remains being given by Bs1 L 2 /Φ0 and the s1 effective lattice spacing by as1 = ls1/ √ 2π where ls1 is the fictitious-magnetic-field length and in our units the fictitious-magnetic-field flux quantum reads Φ0 = 1. Elsewhere it is found that the use of the square-lattice quantum liquid of charge c fermions and spin-neutral two-spinon s1 fermions investigated here contributes to the further understanding of the role of electronic correlations in the unusual properties of the hole-doped cuprate superconductors. This indicates that quantum-Hall-type behavior with or without magnetic field may be ubiquitous in nature.

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“…where A = 1 2 e −∆τ U/4 and α is defined by the relation cosh(∆τ α) = exp(∆τ U/2) 66,75,76 . In the absence of the e-ph interaction, the trace over fermion degrees of freedom can be performed and the partition function is expressed as a product of determinants 75…”

Section: A the Hubbard-holstein Modelmentioning

confidence: 99%

“…The single-band Hubbard model has strong Q = (π/a, π/a) correlations which favor single occupation of the sites. 66 Conversely, the single-band Holstein model exhibits a Q = (π/a, π/a) CDW phase transition at finite temperature. 67,68 In the CDW ordered phase the lattice sites are doubly occupied in a checkerboard pattern.…”

Section: Introductionmentioning

confidence: 99%

Determinant quantum Monte Carlo study of the two-dimensional single-band Hubbard-Holstein model

et al. 2013

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We have performed numerical studies of the Hubbard-Holstein model in two dimensions using determinant quantum Monte Carlo (DQMC). Here we present details of the method, emphasizing the treatment of the lattice degrees of freedom, and then study the filling and behavior of the fermion sign as a function of model parameters. We find a region of parameter space with large Holstein coupling where the fermion sign recovers despite large values of the Hubbard interaction. This indicates that studies of correlated polarons at finite carrier concentrations are likely accessible to DQMC simulations. We then restrict ourselves to the half-filled model and examine the evolution of the antiferromagnetic structure factor, other metrics for antiferromagnetic and charge-density-wave order, and energetics of the electronic and lattice degrees of freedom as a function of electron-phonon coupling. From this we find further evidence for a competition between charge-density-wave and antiferromagnetic order at half-filling.

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Numerical study of the two-dimensional Hubbard model

Cited by 926 publications

References 14 publications

Magnetic and pairing properties of a two-orbital model for the pnictide superconductors: a quantum Monte Carlo study

Magnetic and pairing properties of a two-orbital model for the pnictide superconductors: a quantum Monte Carlo study

The square-lattice quantum liquid of charge c fermions and spin-neutral two-spinon s1 fermions

Determinant quantum Monte Carlo study of the two-dimensional single-band Hubbard-Holstein model

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