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arXiv:cond-mat/9703049

Quantum critical exponents of a planar antiferromagne

Matthias Troyer, Masatoshi Imada

Published Mar 5, 1997• 0 citations
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Abstract

We present high precision estimates of the exponents of a quantum phase transition in a planar antiferromagnet. This has been made possible by the recent development of cluster algorithms for quantum spin systems, the loop algorithms. Our results support the conjecture that the quantum Heisenberg antiferromagnet is in the same universality class as the O(3) nonlinear sigma model. The Berry phase in the Heisenbrg antiferromagnet do not seem to be relevant for the critical behavior.

DOI
10.48550/arxiv.cond-mat/9703049

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We present high precision estimates of the exponents of a quantum phase transition in a planar antiferromagnet. This has been made possible by the recent development of cluster algorithms for quantum spin systems, the loop algorithms. Our results support the conjecture that the quantum Heisenberg antiferromagnet is in the same universality class as the O(3) nonlinear sigma model. The Berry phase in the Heisenbrg antiferromagnet do not seem to be relevant for the critical behavior.
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We simulate the spin-1/2 Heisenberg model with a spatially staggered anisotropy using first principles Monte Carlo method. In particular, the critical exponents β/νβ/νβ/ν and ωωω associated with the quantum phase transition induced by dimerization are determined with high precision. Here βββ and ννν are the exponents related to the magnetization and the correlation length, respectively. In addition, ωωω is the confluent exponent. With very accurate data of the relevant observables, we first obtain a value of ωωω compatible with the known result in the O(3) universality class. Further, using either the value of ωωω determined here or the established one in the literature, the exponent β/νβ/νβ/ν calculated from our data is in quantitative agreement with the known result β/ν=0.519(1)β/ν= 0.519(1)β/ν=0.519(1) as well. Our investigation suggests that the quantum phase transition studied here is fully consistent with the O(3) universality class.
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