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Physical review. B, Condensed matter

Spin correlations in the two-dimensional quantums=1/2XYmodel

J. Szṅajd

Published Aug 1, 1995• 3 citations
Publisher

Abstract

A quantum version of the Niemeijer--van Leeuwen real-space renormalization-group method is used to study the temperature dependence of the two- and four-spin correlations in the quantum XY model on the triangular lattice. The first-order cumulant expansion results suggest, similarly to other methods, a low-temperature phase of an essentially different kind from that predicted for the classical model. The possible explanation of the origin of the spurious 2D Heisenberg-like nontrivial fixed point in some renormalization-group calculations is also proposed.

DOI
10.1103/physrevb.52.4313

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The phase transition of the classical XY\mathrm{XY}XY model on a triangular lattice is studied with a renormalization-group technique based on the cumulant-expansion method of Niemeijer and van Leeuwen. By utilization of some approximations, a nontrivial fixed point is located, and this yields the following critical values: JkTc=0.25\frac{J}{k{T}_{c}}=0.25kTc​J​=0.25, $\ensuremath{\nu}=1.35$, and $\ensuremath{\eta}=0.21$.
The two-dimensional XY\mathrm{XY}XY and Heisenberg models are studied with a quantum-mechanical generalization of the Niemeijer and Van Leeuween renormalization-group method. In second-order cumulant expansion a fixed point exists for the XY\mathrm{XY}XY model, giving a critical temperature at $\frac{J}{k{T}_{c}}\ensuremath{\cong}0.87\ifmmode\pm\else\textpm\fi{}0.05$. For the Heisenberg model we find a fixed point at K∗=2.8{K}^{*}=2.8K∗=2.8. This result may not be reliable, since the truncation of the cumulant expansion is only valid for small KKK.
A new formulation of the renormalization-group in real space, suitable for quantum spin systems is proposed. The method is applied to the two-dimensional spin-12\frac{1}{2}21​ $X\ensuremath{-}Y$ model on a triangular lattice, the renormalization-group transformation being evaluated up to second order in an appropriate cumulant expansion. To first order an unstable fixed point of the transformation is found, corresponding to a critical temperature and critical indices in satisfactory qualitative agreement with present high-temperature series expansion estimates. In the second-order calculation, however, this fixed point disappears, thus throwing some doubt on the conventional picture of criticality as furnished by high-temperature series. The free energy of the model is also computed. For relatively small values of the nearest-neighbor coupling it is in good agreement with that found by high-temperature series analysis.
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