Superconducting ground state of the two-dimensional Hubbard model: A variational study

Eichenberger, David; Baeriswyl, D.

doi:10.1016/j.physc.2007.03.366

Cited by 3 publications

(5 citation statements)

References 8 publications

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“…It is known that the addition of an operator involving the kinetic energy yields an order of magnitude improvement of the ground state energy with respect to a wave function with a Gutzwiller projector alone [14]. In this letter, we show that such an additional term allows us to draw an appealing picture of the ground state, both at half filling and as a function of doping (some preliminary results have been published [15,16]). …”

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confidence: 72%

“…Our mean-field reference state is the BCS wave function with d-wave symmetry, |Ψ 0 = |dBCS , characterized by a gap parameter ∆ describing pairing and a "chemical potential" µ fixing the average electron density n [15]. To reduce the statistical error in the Monte Carlo simulations and consequently the computational time, a fixed set of "Ising spin" configurations is first generated and then used to optimize the variational parameters [20,21].…”

mentioning

confidence: 99%

“…µ fixing the average electron density n [15]. To reduce the statistical error in the Monte Carlo simulations and consequently the computational time, a fixed set of "Ising spin" configurations is first generated and then used to optimize the variational parameters [20,21].…”

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confidence: 99%

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Superconductivity and antiferromagnetism in the two-dimensional Hubbard model: A variational study

Eichenberger

Baeriswyl

2007

Phys. Rev. B

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A variational ground state of the repulsive Hubbard model on a square lattice is investigated numerically for an intermediate coupling strength (U = 8t) and for moderate sizes (from 6 × 6 to 10 × 10). Our ansatz is clearly superior to other widely used variational wave functions. The results for order parameters and correlation functions provide new insight for the antiferromagnetic state at half filling as well as strong evidence for a superconducting phase away from half filling.PACS numbers: 71.10. Fd,74.20.Mn, The Hubbard model plays a key role in the analysis of correlated electron systems, and it is widely used for describing quantum antiferromagnetism, the Mott metalinsulator transition and, ever since Anderson's suggestion [1], superconductivity in the layered cuprates. Several approximate techniques have been developed to determine the various phases of the two-dimensional Hubbard model. For very weak coupling, the perturbative Renormalization Group extracts the dominant instabilities in an unbiased way, namely antiferromagnetism at half filling and d-wave superconductivity for moderate doping [2,3]. Quantum Monte Carlo simulations have been successful in extracting the antiferromagnetic correlations at half filling [4,5], but in the presence of holes the numerical procedure is plagued by the fermionic minus sign problem [6]. This problem appears to be less severe in dynamic cluster Monte Carlo simulations, which exhibit a clear tendency towards d-wave superconductivity for intermediate values of U [7].Variational techniques address directly the ground state and thus offer an alternative to quantum Monte Carlo simulations, which are limited to relatively high temperatures. Previous variational wave functions include mean-field trial states from which configurations with doubly occupied sites are either completely eliminated (full Gutzwiller projection) [8,9,10] or at least partially suppressed [11]. Recently, more sophisticated wave functions have been proposed, which include, besides the Gutzwiller projector, non-local operators related to charge and spin densities [12,13]. Our own variational wave function is based on the idea that for intermediate values of U the best ground state is a compromise between the conflicting requirements of low potential energy (small double occupancy) and low kinetic energy (delocalization). It is known that the addition of an operator involving the kinetic energy yields an order of magnitude improvement of the ground state energy with respect to a wave function with a Gutzwiller projector alone [14]. In this letter, we show that such an additional term allows us to draw an appealing picture of the ground state, both at half filling and as a function of doping (some preliminary results have been published [15,16]).In its most simple form, the 2D Hubbard model is composed of two terms,Ĥ = tT + UD , witĥHere c † iσ creates an electron at site i with spin σ, the summation is restricted to nearest-neighbor sites and n iσ = c † iσ c iσ . We consider a square lattice with peri...

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Superconductivity and antiferromagnetism in the two-dimensional Hubbard model: A variational study

Eichenberger

Baeriswyl

2007

Phys. Rev. B

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“…Instead of this 'grand-canonical' set-up one could also work with a BCS state projected onto a fixed number of particles, where µ becomes a fourth variational parameter. Unfortunately, the minus sign problem turns out to be severe in the 'canonical' case [62], presumably because |BCS N is a correlated state, whereas the conventional BCS wave function can be written as a single Slater determinant. The results discussed below have all been obtained using the grand-canonical version.…”

Section: Superconductivitymentioning

confidence: 99%

“…Unfortunately, the minus sign problem turns out to be severe in the 'canonical' case [62], presumably because |BCS N is a correlated state, whereas the conventional BCS wave function can be written as a single Slater determinant. The results discussed below have all been obtained using the grand-canonical version.…”

Section: Superconductivitymentioning

confidence: 99%

Variational ground states of the two-dimensional Hubbard model

2009

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Recent refinements of analytical and numerical methods have improved our understanding of the ground-state phase diagram of the two-dimensional (2D) Hubbard model. Here we focus on variational approaches, but comparisons with both Quantum Cluster and Gaussian Monte Carlo methods are also made. Our own ansatz leads to an antiferromagnetic ground state at half filling with a slightly reduced staggered order parameter (as compared to simple mean-field theory). Away from half filling, we find d-wave superconductivity, but confined to densities where the Fermi surface passes through the antiferromagnetic zone boundary (if hopping between both nearest-neighbour and next-nearest-neighbour sites is considered). Our results agree surprisingly well with recent numerical studies using the Quantum Cluster method. An interesting trend is found by comparing gap parameters ∆ (antiferromagnetic or superconducting) obtained with different variational wave functions. ∆ varies by an order of magnitude and thus cannot be taken as a characteristic energy scale. In contrast, the order parameter is much less sensitive to the degree of sophistication of the variational schemes, at least at and near half filling.

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Quantum Fluctuations due to Spinons, Polarons, and Stripes in the Two-Dimensional Hubbard Model

Tomita

Watanabe

2009

Phys. Rev. Lett.

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Quantum fluctuations (QF's) in the two-dimensional Hubbard model are visualized by superposition of optimized nonorthogonal Slater determinants. In the half-filled system, QF's consist of rotational and translational motions of spinon-antispinon pairs, while in the lightly doped systems (delta=0.96), those motions of polarons form the QF's. It is shown that an attractive interaction works between two polarons, in the framework of a projected Hartree-Fock picture. At about 10% doping, the ground state has a stripe structure and QF's due to deviations from the uniform stripe. The present method gives the ground state energies comparable or in some cases superior to the variational Monte Carlo method with a Gutzwiller projection parameter.

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Superconducting ground state of the two-dimensional Hubbard model: A variational study

Cited by 3 publications

References 8 publications

Superconductivity and antiferromagnetism in the two-dimensional Hubbard model: A variational study

Superconductivity and antiferromagnetism in the two-dimensional Hubbard model: A variational study

Variational ground states of the two-dimensional Hubbard model

Quantum Fluctuations due to Spinons, Polarons, and Stripes in the Two-Dimensional Hubbard Model

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