Variational Monte Carlo Studies of the Hubbard Model in One- and Two-Dimensions –Off-Diagonal Intersite Correlation Effects–

Otsuka, Hiromi

doi:10.1143/jpsj.61.1645

Cited by 52 publications

(50 citation statements)

References 19 publications

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“…parameter h reduces significantly the total energy, in agreement with similar earlier work [15,16]. The parent state |dBCS〉 is a BCS state with d-wave symmetry, i.e.,…”

Section: A Refined Variational Wave Functionsupporting

confidence: 89%

Superconductivity in the two‐dimensional Hubbard model?

Baeriswyl¹,

Eichenberger²,

Gut³

2007

Physica Status Solidi (b)

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A refined variational wave function for the two-dimensional repulsive Hubbard model is studied numerically, with the aim of approaching the difficult crossover regime of intermediate values of U. The issue of a superconducting ground state with d-wave symmetry is investigated for an average electron density n=0.8125 and for U=8t. Due to finite-size effects a clear-cut answer to this fundamental question has not yet been reached.Comment: 5 pages, 1 figure, Proc. 30th Int. Conf. of Theoretical Physics, Ustron, Poland, 2006, to be published in phys. stat. so

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“…parameter h reduces significantly the total energy, in agreement with similar earlier work [15,16]. The parent state |dBCS〉 is a BCS state with d-wave symmetry, i.e.,…”

Section: A Refined Variational Wave Functionsupporting

confidence: 89%

Superconductivity in the two‐dimensional Hubbard model?

Baeriswyl¹,

Eichenberger²,

Gut³

2007

Physica Status Solidi (b)

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“…As an alternative there exist variational approximations at T = 0 to which we can compare our data. A very promising variational ansatz is provided by a generalized Baeriswil-Gutzwiller wave-function [39]. In Fig.…”

Section: Resultsmentioning

confidence: 99%

Spin and charge structure factor of the two-dimensional Hubbard model

1997

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The spin and charge structure factors are calculated for the Hubbard model on the square lattice near half-filling using a spin-rotation invariant six-slave boson representation. The charge structure factor shows a broad maximum at the zone corner and is found to decrease monotonically with increasing interaction strength and electron density and increasing temperature. The spin structure factor develops with increasing interaction two incommensurate peaks at the zone boundary and along the zone diagonal. Comparison with results of Quantum Monte Carlo and variational calculations is carried out and the agreement is found to be good. The limitations of an RPA-type approach are pointed out.Soon after the discovery of superconductivity in the cuprate materials, it was suggested [1] that this phenomenon is closely related to strong correlation effects. Indeed correlations are responsible for the insulating state observed in the parent compounds. The simplest Hamiltonian accounting for such Mott insulators is the one band Hubbard model. It poses a serious challenge to the theoretician since ordinary many-body perturbation theory breaks down for strong coupling, being unable to account for Mott insulator state. A number of new techniques have been developed, either fully numerical such as Quantum Monte Carlo calculations or exact diagonalizations of small systems [2], or analytical using the Hubbard X-operator technique (for a recent work see [3]), the self-consistent 2-particle theory [4], the dynamical mean field approximation [5] or slave bosons. The slave boson method has been applied to a whole range of problems with local Coulomb interaction: the Kondo impurity model [6,7], the Kondo lattice model [7-10], the Anderson Hamiltonian [6,11] the Hubbard model [12,13] possibly with orbital degeneracy [14] and even the Bose-Hubbard model [15]. In the Kotliar and Ruckenstein (KR) slave boson technique [12] the Gutzwiller Approximation [16-19] appears as a saddle-point approximation of this field theoretical representation of the Hubbard model. In the latter a metal-insulator transition occurs at half-filling in the paramagnetic phase as discussed by Lavagna [20]. The contribution of the thermal fluctuations has been calculated [21] and turned out to be incomplete as this representation, even though exact, is not manifestly spin-rotation invariant. Spin-rotation invariant [22] and spin and charge-rotation invariant [23] formulations have been proposed, all sharing the advantage of treating all the atomic states on an equal footing, and the first one was used to calculate correlation functions [24] and spin fluctuation contributions to the specific heat [25]. Comparisons of ground state energy with Quantum Monte-Carlo simulations, including antiferromagnetic ordering [26] and spiral states [27], or with exact diagonalization data [28] have been done and yield excellent agreement, and a magnetic phase diagram has been proposed [29,30]. The magnetic susceptibility has been evaluated [31] and

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“…͑2͒ promotes delocalization and yields a substantial improvement with respect to the Gutzwiller wave function ͑h =0͒. In fact, it has been demonstrated that ansatz ͑2͒ is very close to the exact ground state both for small 2D systems 6 and for the solvable 1 / r chain. 7 In our previous study of the simple Hubbard model ͑t ij = t for nearest-neighbor sites and 0 otherwise͒, 8 we have found that wave function ͑2͒ exhibits d-wave pairing below a hole concentration of 0.18.…”

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confidence: 96%

Electron doping and superconductivity in the two-dimensional Hubbard model

Eichenberger

Baeriswyl

2009

Phys. Rev. B

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An elaborate variational wave function is used for studying superconductivity in the ͑repulsive͒ twodimensional Hubbard model, including both nearest-and next-nearest-neighbor hoppings. A marked asymmetry is found between the "localized" hole-doped region and the more itinerant electron-doped region. Superconductivity with d-wave symmetry turns out to be restricted to densities where the Fermi surface crosses the magnetic zone boundary. A concomitant peak in the magnetic structure factor at ͑ , ͒ clearly points to a magnetic mechanism.One of the central issues in the field of high-temperature superconductors has been-and for some researchers still is-the question whether pairing in the cuprates arises from purely repulsive interactions, as proposed by Anderson two decades ago. 1 This question has been studied extensively in the framework of the two-dimensional ͑2D͒ ͑repulsive͒ Hubbard model ͑and the related t-J model͒. Recent progress, both in dynamical mean-field theory 2,3 and in variational calculations, 4 has strengthened the case for the existence of a superconducting phase in the Hubbard model, with a ͑d-wave͒ gap parameter reasonably close to the experimental values for intermediate interaction strengths ͑U of the order of the bandwidth͒. This conclusion has been challenged on the basis of Monte Carlo simulations, 5 which we believe to be not conclusive, as discussed below.Most previous studies of the Hubbard model have been restricted to nearest-neighbor hopping, where electron doping does not differ from hole doping. Here we show that the addition of second-neighbor hopping ͑which breaks the electron-hole symmetry͒ changes this behavior substantially. While the hole-doped side is "localized" and shows kineticenergy-driven superconductivity with a large condensation energy, the electron-doped side is itinerant with a potentialenergy-driven superconductivity and a small condensation energy.The Hubbard Hamiltonian Ĥ = Ĥ 0 + UD consists of a hopping term ͑"kinetic energy"͒and an on-site repulsion UD , where D = ͚ i n i↑ n i↓ is the number of doubly occupied sites, n i = c i † c i , and the operator c i † ͑c i ͒ creates ͑annihilates͒ an electron at site i with spin . We use the trial ground statewhere g and h are ͑real͒ variational parameters and ͉⌿ 0 ͘ is a BCS state with d-wave symmetry. The first term in Eq. ͑2͒ promotes delocalization and yields a substantial improvement with respect to the Gutzwiller wave function ͑h =0͒. In fact, it has been demonstrated that ansatz ͑2͒ is very close to the exact ground state both for small 2D systems 6 and for the solvable 1 / r chain. 7In our previous study of the simple Hubbard model ͑t ij = t for nearest-neighbor sites and 0 otherwise͒, 8 we have found that wave function ͑2͒ exhibits d-wave pairing below a hole concentration of 0.18. At first sight this result seems to contradict recent Monte Carlo simulations, 5 where no signature for superconductivity was found, but a closer look shows that there is no discrepancy. In fact, three of the four hole densities consid...

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Variational Monte Carlo Studies of the Hubbard Model in One- and Two-Dimensions –Off-Diagonal Intersite Correlation Effects–

Cited by 52 publications

References 19 publications

Superconductivity in the two‐dimensional Hubbard model?

Superconductivity in the two‐dimensional Hubbard model?

Spin and charge structure factor of the two-dimensional Hubbard model

Electron doping and superconductivity in the two-dimensional Hubbard model

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