Ground-state energy of the Hubbard model at half filling

Polatsek, G.; Becker, K. W.

doi:10.1103/physrevb.54.1637

Cited by 14 publications

(12 citation statements)

References 21 publications

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“…In Table I the results obtained by minimizing the energy expectation value with respect to the three variational parameters g, h, ∆ AF for an 8 × 8 lattice are compared with the unrestricted Hartree-Fock approximation (g = h = 0), the Gutzwiller wave function (g > 0, h = 0) [17], a quantum Monte Carlo simulation [4] and a Projector Operator technique [18]. The gap parameter ∆ AF is very large for g = h = 0 and decreases dramatically if g and h are optimized.…”

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confidence: 99%

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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“…Note that the slight increase in the relative error with increasing U at least partially has to be attributed to the circumstance that the QMC calculations become less exact with increasing U. Also in Fig [6] (see also [5], [7], [8] and [9] with similar results). The relative difference is less than 0.08% (see also Table 1).…”

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confidence: 58%

“…Thus H 0 is a set of horizontally alligned noninteracting dimers. Note that H 0 already contains all correlation terms of (5). The terms H n are then the missing bonds i.e.…”

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Incremental expansions for the ground-state energy of the two-dimensional Hubbard model

1999

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A generalization of Faddeev's approach of the 3-body problem to the manybody problem leads to the method of increments. This method was recently applied to account for the ground state properties of Hubbard-Peierls chains (JETP Letters 67 (1998) 1052). Here we generalize this approach to twodimensional square lattices and explicitely treat the incremental expansion up to third order. Comparing our numerical results with various other approaches (Monte Carlo, cumulant approaches) we show that incremental expansions are very efficient because good accuracy with those approaches is achieved treating lattice segments composed of 8 sites only.

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“…For this reason it has previously been used to study strongly correlated electronic systems. [6][7][8] The introduction of cumulants ensures that expressions of physical quantities are always ''size consistent.'' For example, this implies that expectation values of extensive variables scale proportionally to the system size.…”

Section: Cumulant Approachmentioning

confidence: 99%

Construction of size-consistent effective Hamiltonians

Polatsek

Becker

1997

Phys. Rev. B

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For a system consisting of two interacting subsystems, effective Hamiltonians for one subsystem are usually constructed by integrating out the degrees of freedom of the second subsystem. In contrast to usual treatments, our method for deriving effective Hamiltonians is based on the introduction of cumulants. Cumulants guarantee size consistency, a property that is not always evident in other approaches. The formalism applies for any temperature. Our method is based on a matrix formulation in the framework of a recently introduced cumulantprojection method. This method allows the treatment of strongly correlated systems, where conventional diagrammatic techniques are difficult to apply. The relation with perturbation theory is also shown. As a simple application we discuss the small polaron problem. Evaluating the one-electron dispersion relation in the strong-coupling case shows good agreement with recent results from exact Lanczos diagonalization. Our method has substantial advantages over perturbation theory.

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Ground-state energy of the Hubbard model at half filling

Cited by 14 publications

References 21 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

Incremental expansions for the ground-state energy of the two-dimensional Hubbard model

Construction of size-consistent effective Hamiltonians

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