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arXiv:cond-mat/9506078

Variational Monte Carlo Studies of t-J-type Models

Hisatoshi Yokoyama, Yoshio Kuramoto, Masao Ogata

Published Jun 19, 1995• 0 citations
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Abstract

We give a brief review of recent developments by the variational Monte Carlo method, in addition to some new results. We discuss $t$-$J$-type models: the ordinary $t$-$J$ model in one and two dimensions, and the one-dimensional supersymmetric $t$-$J$ model with the long-range coupling of inverse square.

DOI
10.48550/arxiv.cond-mat/9506078

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We give a brief review of recent developments by the variational Monte Carlo method, in addition to some new results. We discuss ttt-JJJ-type models: the ordinary ttt-JJJ model in one and two dimensions, and the one-dimensional supersymmetric ttt-JJJ model with the long-range coupling of inverse square.
As a continuation of a previous paper [J. Phys. Soc. Jpn. 56 (1987) 1490], the variational Monte-Carlo method is extended to include the antiferromagnetic long-range order. The theory is based on the Gutzwiller-type correlation factor and its effect is exactly taken into account by the Monte-Carlo procedure. An application is made to the half-filled-band case of one-dimensional lattice (50 sites), two-dimensional square lattice (up to 20×20 sites) and three-dimensional simple cubic lattice (6×6×6 sites). The result is qualitatively different from previous studies relying on the random-phase-type "Gutzwiller approximation." The variational energy for two and three dimensions is favorably compared with Hirsch's quantum Monte-Carlo data.
Using Monte Carlo simulation, the one dimensional N-state clock model with long range inverse square interaction has been studied. In the case of N = 6, the temperature dependence of the specific heat shows two peaks at T1 and T2 (< T1). The critical exponent η calculated from the system size dependence of magnetization changes with temperature in the region between T1 and T2. The behaviors are very similar to those of the two-dimensional 6-state clock model with the nearest neighbor interaction which shows two steps of phase transition, Berezinskii-Kosterlitz-Thouless transition and ordinary long range order. We have also confirmed that the temperature T2 shift toward zero with the increase of N.
A set of generalized Gutzwiller-type wave functions with spin and charge currents and/or spin polarization are shown to be exact eigenstates of the supersymmetric t - J -type model with long-range interactions. The increment of energy in the presence of currents is proportional to the square of the currents without any higher-order corrections for arbitrary size of the system. The exact excited states are identified by the absence of statistical fluctuations in the variational Monte Carlo calculation. The spin susceptibility is found to be independent of the size, as in the case of the charge susceptibility.