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Physica A Statistical Mechanics and its Applications

The long-range ordering in a quantum lattice gas

Boris Volodumurovich Bondarev

Published Sep 1, 1994• 3 citations
Publisher
DOI
10.1016/0378-4371(94)90198-8

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A method is developed for the exact high temperature series expansion of thermodynamic properties of the spin 1/2 XY model of ferromagnetism or of a quantum lattice gas. Eleven coefficients in the specific heat series for the f.c.c. and b.c.c. lattices and nine coefficients in the series for the fluctuation in the long range order for the f.c.c., b.c.c., and s.c. lattices are calculated. From the fluctuation series the critical temperatures Kc−1 ≡ kTc/J are estimated to be 4.520, 2.902, and 2.02 respectively, while the critical index for the square of the fluctuation in the long range order is γ = 1.35.
The lattice model with short‐range interactions (exemplified by the Hubbard model) is known to exhibit quite different features from those in the electron gas with the long‐range Coulomb interaction. In order to explore how they cross over to each other, we have studied an extended Hubbard model which includes repulsions up to the 12th neighbors with the simplified fluctuation exchange (FLEX) approximation for the square lattice. We have found that (i) in the most dilute density region, spin and charge fluctuations become comparable, and s‐ and p‐waves superconductivity become dominant, in agreement with the result for the electron gas by Takada, while (ii) the dominant spin fluctuation and its reflection on dx2−y2 and dxy pairing, both the effect of lattice structure, persists well away (n ≳ 0.2) from the half filling. © 2006 American Institute of Physics
The relationship among the Wigner crystal, charge ordering, and the Mott insulator is studied by the path-integral renormalization group method in two-dimensional systems with long-range Coulomb interaction. In contrast to the insensitivity of the Hartree-Fock results, the stability of the solid drastically decreases with the decrease in the lattice commensurability. The transition to liquid occurs at the electron gas parameter r(s) approximately 2 for the filling n=1/2, showing a large reduction from r(s) approximately 35 in the continuum limit. A correct account of quantum fluctuations is crucial to understanding the charge-order stability generally observed only at simple fractional fillings and the nature of quantum liquids away from them.