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physica status solidi (b)

On the extended hubbard model in one dimension

P. Gluck

Published Nov 1, 1982• 0 citations
Publisher
DOI
10.1002/pssb.2221140143

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The one-dimensional Hubbard model is known to possess an extended su(2) symmetry and to be integrable. I indroduce an integrable model with an extended su(n) symmetry. This model contains the usual su(2) Hubbard model and has a set of features that make it the su(n) generalization of the Hubbard model. Complete integrability is shown by introducing the L-matrix and showing that the transfer matrix commutes with the hamiltonian. While the model is integrable in one dimension, it provides a generalization of the Hubbard hamiltonian in any dimension.
Applicability of the Hubbard model (HM) to one-dimensional solids is investigated by careful analysis of the introduced approximations and by analytical calculation of the integrals. Consistency with the other approximations implies the neglect of interbond-charge-repulsion integrals. If the interelectronic potential is long range, the extended HM is adequate. On the contrary, for highly screened potentials intersite charge repulsion terms loose their importance in favor of the bond-site terms. The extended HM is then replaced by a new model, which in the mean-field treatment reduces to the simple HM.
We present results of quantum Monte Carlo simulations for the soft-core extended bosonic Hubbard model in one dimension exhibiting the presence of supersolid phases similar to those recently found in two dimensions. We find that in one and two dimensions, the insulator-supersolid transition has dynamic critical exponent z = 2 whereas the first order insulator-superfluid transition in two dimensions is replaced by a continuous transition with z = 1 in one dimension. We present evidence that this transition is in the Kosterlitz-Thouless universality class and discuss the mechanism behind this difference. The simultaneous presence of two types of quasi-long-range order results in two solitonlike dips in the excitation spectrum.