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arXiv:cond-mat/9709333 · Physical Review Letters

Low Temperature Behavior and Crossovers of the Square Lattice Quantum Heisenberg Antiferromagnet

Jae-Kwon Kim, Matthias Troyer

Published Mar 23, 1998• 151 citations
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Abstract

We present thermodynamic measurements of various physical observables of the two-dimensional $S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2$ isotropic quantum Heisenberg antiferromagnet on a square lattice, obtained by quantum Monte Carlo methods. The results are in excellent agreement with field-theoretical predictions. The issue of the existence of a crossover from quantum critical to renormalized classical regime is clarified.

DOI
10.1103/physrevlett.80.2705

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The Antiferromagnetic Heisenberg Model with spin 1/2 on a square lattice was simulated by using the Stochastic Series Expansion(SSE) Quantum Monte Carlo Method.The temperature dependence of the internal energy,specific heat and uniform susceptibility was observed.The results showed that specific heat has a maximum at kT/J=0.6 and uniform susceptibility saturates at kT/J=1 for the isotropy case.And the size of lattice also affects the temperature dependence of these thermodynamic quantities.For the anisotropy case,energy decreases with anisotropic parameter g increasing.Susceptibility changes slowly with temperature for g1 and exponentially decay for g1 in the low temperature region and its behaviors approach consistent for different g in the high temperature region.
Abstract We consider the S = 1/2 Heisenberg antiferromagnet on the Tasaki square lattice (flat-band spin system) and study its low-temperature thermodynamics around the saturation magnetic field. To this end, we construct a mapping of the ground states in the subspaces with total S z = N /2, …, N /3 ( N is the number of lattice sites) on the hard squares on an auxiliary square lattice and use classical Monte Carlo simulations to examine the latter classical system. The most prominent feature of the S = 1/2 Heisenberg antiferromagnet on the Tasaki square lattice under consideration is an order-disorder phase transition which occurs at a low temperature just below the saturation magnetic field and belongs to the 2D Ising universality class.