Exact solution and thermodynamics of the Hubbard model with infinite-range hopping

Dongen, Peter van; Vollhardt, D.

doi:10.1103/physrevb.40.7252

Cited by 35 publications

(19 citation statements)

References 10 publications

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“…Here we generalize the results by van Dongen and Vollhardt [14] to the case of a non-extensive number of non-vanishing one-body eigenenergies and in the presence of a local external magnetic field coupled to the spin of the particles. Even if the reasoning is similar to that of Ref.…”

Section: Thermodynamic Limitsupporting

confidence: 61%

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Antiferromagnetism in the exact ground state of the half-filled Hubbard model on the complete bipartite graph

Stefanucci

Cini

2002

Phys. Rev. B

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As a prototype model of antiferromagnetism, we propose a repulsive Hubbard Hamiltonian defined on a graph Λ = A∪B with A∩B = ∅ and bonds connecting any element of A with all the elements of B. Since all the hopping matrix elements associated with each bond are equal, the model is invariant under an arbitrary permutation of the A-sites and/or of the B-sites. This is the Hubbard model defined on the so called (NA, NB)-complete-bipartite graph, NA (NB) being the number of elements in A (B). In this paper we analytically find the exact ground state for NA = NB = N at half filling for any N ; the ground state expectation value of the repulsion term has a maximum at a critical N -dependent value of the on-site Hubbard U and then drops like 1/U for large U . The wave function and the energy of the unique, singlet ground state assume a particularly elegant form for N → ∞. We also calculate the spin-spin correlation function and show that the ground state exhibits an antiferromagnetic order for any non-zero U even in the thermodynamic limit. This is the first explicit analytic example of an antiferromagnetic ground state in a Hubbard-like model of itinerant electrons. The kinetic term induces non-trivial correlations among the particles and an antiparallel spin configuration in the two sublattices comes to be energetically favoured at zero Temperature. On the other hand, if the thermodynamic limit is taken and then zero Temperature is approached, a paramagnetic behavior results. The thermodynamic limit does not commute with the zero-Temperature limit, and this fact can be made explicit by the analytic solutions.

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Section: Thermodynamic Limitsupporting

confidence: 61%

“…This model was numerically studied by Patterson on small clusters [13] in 1972 and solved in the thermodynamic limit by van Dongen and Vollhardt [14] only at the end of the eighties. Much more effort was needed to find the exact ground state(s) in the finite-size system.…”

Section: Introductionmentioning

confidence: 99%

Antiferromagnetism in the exact ground state of the half-filled Hubbard model on the complete bipartite graph

Stefanucci

Cini

2002

Phys. Rev. B

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“…13,41 This is also called the limit of "infinite-range hopping". 13,41,42 The free energy density of the bosonic Hubbard model in this limit has the form…”

Section: B Immobile Bosons ("Atomic Limit")mentioning

confidence: 99%

Correlated bosons on a lattice: Dynamical mean-field theory for Bose-Einstein condensed and normal phases

2008

Self Cite

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We formulate a bosonic dynamical mean-field theory (B-DMFT) which provides a comprehensive, thermodynamically consistent framework for the theoretical investigation of correlated lattice bosons. The B-DMFT is applicable for arbitrary values of the coupling parameters and temperature and becomes exact in the limit of high spatial dimensions d or coordination number Z of the lattice. In contrast to its fermionic counterpart the construction of the B-DMFT requires different scalings of the hopping amplitudes with Z depending on whether the bosons are in their normal state or in the Bose-Einstein condensate. A detailed discussion of how this conceptual problem can be overcome by performing the scaling in the action rather than in the Hamiltonian itself is presented. The B-DMFT treats normal and condensed bosons on equal footing and thus includes the effects caused by their dynamic coupling. It reproduces all previously investigated limits in parameter space such as the Beliaev-Popov and Hartree-Fock-Bogoliubov approximations and generalizes the existing mean-field theories of interacting bosons. The self-consistency equations of the B-DMFT are those of a bosonic single-impurity coupled to two reservoirs corresponding to bosons in the condensate and in the normal state, respectively. We employ the B-DMFT to solve a model of itinerant and localized, interacting bosons analytically. The local correlations are found to enhance the condensate density and the Bose-Einstein condensate (BEC) transition temperature TBEC. This effect may be used experimentally to increase TBEC of bosonic atoms in optical lattices.

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“…This special behaviour, absent in any other larger ring, is to be seen as deriving from the anomalous one-dimensional nature of the 3-and the 4-site ring: in the 3-site case the physics is essentially equivalent to that of the Hubbard model with infinite range hopping [8], whereas the 4-site ring represents the only case in which a ring satisfies the connectivity condition in the spin configuration space, as defined in Ref. [3].…”

Section: Resultsmentioning

confidence: 99%

Ferromagnetism in Hubbard Chains

1997

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We analyze the possible occurrence of ferromagnetism in the Hubbard model, by means of an exact diagonalization study performed on 3-to 8-site chains with periodic boundary conditions. In the case of one hole in the half-filled configuration, we find that the Nagaoka state is reached only in the 3-and in the 4-site case. Ground states characterized by unsaturated ferromagnetism are found when the case of more than one hole is considered.

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Exact solution and thermodynamics of the Hubbard model with infinite-range hopping

Cited by 35 publications

References 10 publications

Antiferromagnetism in the exact ground state of the half-filled Hubbard model on the complete bipartite graph

Antiferromagnetism in the exact ground state of the half-filled Hubbard model on the complete bipartite graph

Correlated bosons on a lattice: Dynamical mean-field theory for Bose-Einstein condensed and normal phases

Ferromagnetism in Hubbard Chains

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