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arXiv:cond-mat/9702077 · Journal of the Physical Society of Japan

Critical Exponents of the Quantum Phase Transition in a Planar Antiferromagnet

Matthias Troyer, Masatoshi Imada, Kazuo Ueda

Published Oct 15, 1997• 73 citations
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Abstract

We have performed a large scale quantum Monte Carlo study of the quantum phase transition in a planar spin-1/2 Heisenberg antiferromagnet with CaV4O9 structure. We obtain a dynamical exponent z=1.018+/-0.02. The critical exponents beta, nu and eta agree within our errors with the classical 3D O(3) exponents, expected from a mapping to the nonlinear sigma model. This confirms the conjecture of Chubukov, Sachdev and Ye [Phys. Rev. B 49, 11919 (1994)] that the Berry phase terms in the planar Heisenberg antiferromagnet are dangerously irrelevant.

DOI
10.1143/jpsj.66.2957

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We have performed a large scale quantum Monte Carlo study of the quantum phase transition in a planar spin-1/2 Heisenberg antiferromagnet with CaV4O9 structure. We obtain a dynamical exponent z=1.018+/-0.02. The critical exponents beta, nu and eta agree within our errors with the classical 3D O(3) exponents, expected from a mapping to the nonlinear sigma model. This confirms the conjecture of Chubukov, Sachdev and Ye [Phys. Rev. B 49, 11919 (1994)] that the Berry phase terms in the planar Heisenberg antiferromagnet are dangerously irrelevant.
Quantum phase transition of site-diluted and bond-diluted Heisenberg antiferromagnets on square lattices is studied. By using the novel continuous-time loop algorithm, we perform quantum Monte Carlo simulations on quite larger lattices at extremely lower temperatures than the previous numerical studies. It is found that the antiferromagnetic long-range order at T = 0 persists so long as a cluster of magnetic sites percolates, that is, the critical concentration is equal to the classical percolation threshold, in both of the site-diluted and bond-diluted cases. Furthermore, we find that some critical exponents, such as the magnetization exponent β, are non-classical and strongly depend on the spin size S. On the other hand, we show that the correlation-length exponent ν is universal and is equal to the classical value (ν=4/3).
Critical properties of the two successive phase transitions of Ising-like Heisenberg antiferromagnets on the hexagonal lattice are examined by the Monte Carlo method. In order to obtain the critical exponents, the finite size scaling methods are used for the lattice sizes of L =18 ∼ 48. Using the reweighting Monte Carlo method, the exponents at the higher critical temperature are estimated as 1/ν=1.481±0.019 and γ/ν=1.980±0.016, which agree with those of the 3DXY model. At the lower critical temperature, standard procedure of the reweighting method does not give values of the exponents with satisfactory precision. Thus we estimate the exponents carefully with aid of the ordinary Monte Carlo method at various temperatures near T c . The values of 1/ν≃ 1.48±0.006 and γ/ν≃1.97±0.050 are obtained and we conclude that those are consistent with the universality class of the 3DXY model.
We have simulated the three-dimensional Heisenberg model on simple cubic lattices, using the single-cluster Monte Carlo update algorithm. The expected pronounced reduction of critical slowing down at the phase transition is verified. This allows simulations on significantly larger lattices than in previous studies and consequently a better control over systematic errors. In one set of simulations we employ the usual finite-size scaling methods to compute the critical exponents \ensuremath{\nu},\ensuremath{\alpha},\ensuremath{\beta},\ensuremath{\gamma},\ensuremath{\eta} from a few measurements in the vicinity of the critical point, making extensive use of histogram reweighting and optimization techniques. In another set of simulations we report measurements of improved estimators for the spatial correlation length and the susceptibility in the high-temperature phase, obtained on lattices with up to 1003{100}^{3}1003 spins. This enables us to compute independent estimates of \ensuremath{\nu} and \ensuremath{\gamma} from power-law fits of their critical divergencies.
Puzzled by the indication of a new critical theory for the spin-1/2 Heisenberg model with a spatially staggered anisotropy on the square lattice, as suggested in Wenzel (2008 Phys. Rev. Lett. 101 127202), we study a similar anisotropic spin-1/2 Heisenberg model on the honeycomb lattice. The critical point where the phase transition occurs due to the dimerization as well as the critical exponent ν are analyzed in great detail. Remarkably, using most of the available data points in conjunction with the expected finite-size scaling ansatz with a sub-leading correction indeed leads to a consistent ν = 0.691(2) with that calculated in Wenzel (2008 Phys. Rev. Lett. 101 127202). However, by using the data with a large number of spins N , we obtain ν = 0.707(6) which agrees with the most accurate Monte Carlo O(3) value ν = 0.7112(5) as well.
We present Monte Carlo simulations of a two-dimensional bilayer quantum Heisenberg antiferromagnet with random dimer dilution. In contrast with exotic scaling scenarios found in other random quantum systems, the quantum phase transition in this system is characterized by a finite-disorder fixed point with power-law scaling. After accounting for corrections to scaling, with a leading irrelevant exponent of omega approximately 0.48, we find universal critical exponents z=1.310(6) and nu=1.16(3). We discuss the consequences of these findings and suggest new experiments.