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physica status solidi (b)

Phase transitions in anisotropic two‐dimensional quantum antiferromagnets

Tommaso Roscilde, Alessandro Cuccoli, Paola Verrucchi

Published Mar 1, 2003• 6 citations
Publisher

Abstract

Abstract We study the thermodynamic properties of anisotropic two‐dimensional quantum antiferromagnets, with both easy‐plane and easy‐axis anisotropy. We make use of the Quantum Monte Carlo (QMC) method based on the continuous‐time loop algorithm. For S = 1/2 and very small anisotropies our QMC data reveal that both the Ising and Berezinskii–Kosterlitz–Thouless universality class (for the easy‐axis and easy‐plane models, respectively) are well observed and that the critical temperature remains finite even for anisotropies as small as 10–3, i.e. comparable to the anisotropies measured in real layered compounds; this result rules out the possibility of quantum fluctuations to destroy the finite‐temperature transition before the isotropic limit is reached. The phase diagram of the S = 1/2 2d‐XXZ antiferromagnet in the region of small anisotropies is then presented.

DOI
10.1002/pssb.200301697

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Abstract We study the thermodynamic properties of anisotropic two‐dimensional quantum antiferromagnets, with both easy‐plane and easy‐axis anisotropy. We make use of the Quantum Monte Carlo (QMC) method based on the continuous‐time loop algorithm. For S = 1/2 and very small anisotropies our QMC data reveal that both the Ising and Berezinskii–Kosterlitz–Thouless universality class (for the easy‐axis and easy‐plane models, respectively) are well observed and that the critical temperature remains finite even for anisotropies as small as 10–3, i.e. comparable to the anisotropies measured in real layered compounds; this result rules out the possibility of quantum fluctuations to destroy the finite‐temperature transition before the isotropic limit is reached. The phase diagram of the S = 1/2 2d‐XXZ antiferromagnet in the region of small anisotropies is then presented.
We study the critical and thermodynamic properties of an S=1/2 two-dimensional quantum XXZ antiferromagnet with weak easy-plane anisotropy using the continuous-time quantum Monte Carlo method based on the loop-cluster algorithm. A detailed finite-size scaling analysis reveals that the model displays a finite temperature Berezinskii–Kosterlitz–Thouless (BKT) transition for anisotropy as small as 10−3, the dominant isotropic coupling. For larger anisotropy (10−2) we single out relevant features of anisotropic behavior that anticipate the BKT transition. Implications for experimental observation of a BKT phase in real magnets are discussed.
The critical behavior of 2D magnetic easy-plane systems has mainly been studied by the classical XY model. However, the z components of the spins have to be considered in order to describe real systems, and their fluctuations cannot positively be neglected when quantum effects are to be included, quantum spins being intrinsically three-component objects. Therefore, Monte Carlo simulations are performed for the Heisenberg ferromagnet with easy-plane anisotropy (XXZ model) on a two-dimensional square lattice with a twofold aim: first, to obtain accurate quantitative results about the critical behavior of the classical model, showing the relevant role played by the out-of-plane fluctuations; second, to open the way for approaching the quantum thermodynamics by means of the effective Hamiltonian method that reduces the quantum thermodynamics of the XXZ ferromagnet to the investigation of an effective classical model with temperature-dependent renormalized interaction parameters. Specific heat, magnetic susceptibility, and correlation length are calculated in the critical region for lattice sizes up to 128×128. These quantities preserve the Kosterlitz–Thouless behavior of the XY model. For the transition temperature of the classical XX0 model we obtain the estimate kBTc/(JS̃2)=0.69±0.01.
We consider the quantum easy-plane (XXZ) magnet on the square lattice. In the classical case the system exhibits the Berezinskii–Kosterlitz–Thouless transition. Simulations, both for ferro- and antiferromagnets, using the method of the effective classical Hamiltonian, are made for different spin values and refer to the specific heat, the static spin correlation functions and correlation lengths in a broad range of temperatures, below and above the transition. The effects of quantum fluctuations are quantitatively evaluated and discussed.
Abstract In this work we use numerical Monte Carlo techniques to study the phase diagram of the three‐dimensional classical Heisenberg anti‐ferromagnetic (AF) model with single‐ion anisotropy model with an uniform magnetic field applied along the easy axis. Early experimental as well as theoretical calculations have shown that the phase diagram of the model is quite rich. We simulated the model on a simple cubic lattices using the Wang–Landau sampling and Metropolis algorithm. Finite size scaling theory is used to obtain the phase diagram. At low field and low temperature the system exhibits AF order separated from a spin‐flop (SF) phase by a first‐order line. As temperature grows a paramagnetic phase is reached by crossing a second‐order line both from the AF phase and from the SF phase. The critical exponents are obtained for each transition line. Contrary to early works we find that the line separating the SF phase from the paramagnetic phase is in the Ising class of universality.
The XXZ spin Hamitonian H = - ( S i x S j x + S i y S j y + λ S i z S j z ) is simulated for quantum spins. The XY model (λ = 0) has a Kosterlitz- Thouless Phase transition T KT = 0.45 ± 0.05, slightly above which the specific heat has a finite peak. The vortex density has a non-zero value in the low-temperature limit, probably due to quantum fluctuations. The critical temperature holds up at least to λ = -0.8. The Ising transition temperature T Ising is measured for Ising-like antiferromagnets λ < -1 and is found to drop off to zero in a manner consistent with the reciprocal-logarithmic behavior T c α-1/log|-λ-1|, as proposed for the classical model.
In this paper we present a study of the phase diagram and critical properties of the square-lattice quantum XY model, with a single-ion anisotropy and spin S = 1, as a function of the anisotropy parameter D . For D less than a critical value D C , which is the critical point for a quantum phase transition at T = 0, the model presents a Berezinskii–Kosterlitz–Thouless (BKT) transition. This region is adequately described by the self-consistent harmonic approximation. We show that, if we want to use a Schwinger boson theory in this region, we should include fluctuations around the mean-field approximation (which leads to a gauge field) to describe correctly the BKT transition. However both methods are inadequate to describe the large- D phase, and we show that this phase can be studied using the bond operator formalism which gives the correct behaviour for the correlation length as a function of the temperature in the critical point and above. Our results agree with scaling arguments.