Contour-time approach to the Bose–Hubbard model in the strong coupling regime: Studying two-point spatio-temporal correlations at the Hartree–Fock–Bogoliubov level

As a contribution to the study of the Hartree–Fock theory, we prove rigorously that the Hartree–Fock approximation to the ground state of the d-dimensional Hubbard model leads to saturated ferromagnetism when the particle density (more precisely, the chemical potential μ) is small and the coupling constant U is large, but finite. This ferromagnetism contradicts the known fact that there is no magnetization at low density, for any U, and thus shows that HF theory is wrong in this case. As in the usual Hartree–Fock theory, we restrict attention to Slater determinants that are eigenvectors of the z-component of the total spin, 𝕊z = ∑x nx,↑ - nx,↓, and we find that the choice 2𝕊z = N = particle number gives the lowest energy at fixed 0 < μ < 4d.

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Strong Coupling Regime in the Hubbard Model at Low Densities

Dynamics of Magnetic Fluctuations in High-Temperature Superconductors - NATO ASI Series ◽

10.1007/978-1-4684-7490-9_25 ◽

1991 ◽

pp. 255-259

Author(s):

Alberto Parola ◽

Sandro Sorella ◽

Michele Parrinello ◽

Erio Tosatti

Keyword(s):

Hubbard Model ◽

Strong Coupling ◽

Strong Coupling Regime

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A STRONG-COUPLING EXPANSION FOR THE HUBBARD MODEL

International Journal of Modern Physics B ◽

10.1142/s0217979200002430 ◽

2000 ◽

Vol 14 (24) ◽

pp. 2529-2560 ◽

Cited By ~ 2

Author(s):

N. DUPUIS ◽

S. PAIRAULT

Keyword(s):

Hubbard Model ◽

Strong Coupling ◽

Strong Coupling Expansion ◽

Coulomb Repulsion ◽

Functional Integral ◽

Projection Operators ◽

Hartree Fock ◽

Self Energy ◽

Degenerate Ground State ◽

Component Field

We reconsider the strong-coupling expansion for the Hubbard model recently introduced by Sarker and Pairault et al. By introducing slave particles that act as projection operators onto the empty, singly occupied and doubly occupied atomic states, the perturbation theory around the atomic limit distinguishes between processes that do conserve or do not conserve the total number of doubly occupied sites. This allows for a systematic t/U expansion that does not break down at low temperature (t being the intersite hopping amplitude and U the local Coulomb repulsion). The fermionic field becomes a two-component field, which reflects the presence of the two Hubbard bands. The single-particle propagator is naturally expressed as a function of a 2×2 matrix self-energy. Furthermore, by introducing a time- and space-fluctuating spin-quantization axis in the functional integral, we can expand around a "non-degenerate" ground-state where each singly occupied site has a well defined spin direction (which may fluctuate in time). This formalism is used to derive the effective action of charge carriers in the lower Hubbard band to first order in t/U. We recover the action of the t–J model in the spin-hole coherent-state path integral. We also compare our results with those previously obtained by studying fluctuations around the large-U Hartree–Fock saddle point.

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