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Physical Review Letters

Second-Order Reentrant Phase Transition in the Quantum Anisotropic Planar Rotor Model

Balázs Hetényi, Martin H. Müser, B. J. Berne

Published Nov 29, 1999• 15 citations
Publisher

Abstract

The orientational behavior of the quantum anisotropic planar rotor model is studied by means of the path-integral Monte Carlo method combined with finite size scaling. We compare a system where all angular momentum states are allowed, and one where the angular momentum is restricted to have even values. We find that a reentrant phase transition is present in the unrestricted case, where the system reenters a disordered phase upon cooling. Cumulants that are sensitive to the order of the transition indicate that the phase transition is second order. In the parameter range investigated in this paper, the even angular momentum system does not show reentrance.

DOI
10.1103/physrevlett.83.4606

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The orientational behavior of the quantum anisotropic planar rotor model is studied by means of the path-integral Monte Carlo method combined with finite size scaling. We compare a system where all angular momentum states are allowed, and one where the angular momentum is restricted to have even values. We find that a reentrant phase transition is present in the unrestricted case, where the system reenters a disordered phase upon cooling. Cumulants that are sensitive to the order of the transition indicate that the phase transition is second order. In the parameter range investigated in this paper, the even angular momentum system does not show reentrance.
The ground state properties of the quantum anisotropic planar rotor (QAPR) model, which was constructed to describe the orientational ordering of homonuclear diatomic molecules on inert surfaces, are investigated theoretically using diffusion Monte Carlo. The implementation of the descendant weighing (DW) technique due to Casulleras and Boronat [Phys. Rev. B 52, 3654 (1995)] is used, for which an alternate derivation is presented, based on the path-integral representation of the imaginary time propagator. We calculate the order parameter and then perform finite size scaling in order to search for a critical reduced rotational constant Bc* at zero temperature. Our simulation results indicate that a critical rotational constant is at Bc*≈0.25. The behavior of the kinetic and potential energies show strong evidence for local, single-rotor tunneling as the driving mechanism for the phase transition. A Gaussian mean-field treatment is also presented, in which the most important mechanism is local, single-rotor tunneling. While quantitatively the mean-field phase transition is not in agreement with the simulation results, the energy curves show qualitative similarities. In both cases, the phase transition occurs at the point where the kinetic energy reaches a maximum as a function of the reduced rotational constant B*.
We introduce a path integral Monte Carlo approach that uses the angular momentum representation for the description of interacting rotor systems. Such a choice of representation allows the calculation of momentum properties without having to break the paths. The discrete nature of the momentum basis also allows the use of rejection-free Gibbs sampling techniques. To illustrate the method, we study the collective behavior of N confined planar rotors with dipole-dipole interactions, a system known to exhibit a quantum phase transition from a disordered to an ordered state at zero temperature. Ground state properties are obtained using the path integral ground state method. We propose a Bond-Hamiltonian decomposition for the high temperature density matrix factorization of the imaginary time propagator. We show that cluster-loop type moves are necessary to overcome ergodicity issues and to achieve efficient Markov chain updates. Ground state energies and angular momentum properties are computed and compared with density matrix renormalization group benchmark results. In particular, the derivative of the kinetic energy with respect to the interaction strength estimator is presented as a successful order parameter for the detection of the quantum phase transition.
The quantum phase transitions of dipoles confined to the vertices of two-dimensional lattices of square and triangular geometry is studied using path integral ground state quantum Monte Carlo. We analyze the phase diagram as a function of the strength of both the dipolar interaction and a transverse electric field. The study reveals the existence of a class of orientational phases of quantum dipolar rotors whose properties are determined by the ratios between the strength of the anisotropic dipole-dipole interaction, the strength of the applied transverse field, and the rotational constant. For the triangular lattice, the generic orientationally disordered phase found at zero and weak values of both dipolar interaction strength and applied field is found to show a transition to a phase characterized by net polarization in the lattice plane as the strength of the dipole-dipole interaction is increased, independent of the strength of the applied transverse field, in addition to the expected transition to a transverse polarized phase as the electric field strength increases. The square lattice is also found to exhibit a transition from a disordered phase to an ordered phase as the dipole-dipole interaction strength is increased, as well as the expected transition to a transverse polarized phase as the electric field strength increases. In contrast to the situation with a triangular lattice, on square lattices, the ordered phase at high dipole-dipole interaction strength possesses a striped ordering. The properties of these quantum dipolar rotor phases are dominated by the anisotropy of the interaction and provide useful models for developing quantum phases beyond the well-known paradigms of spin Hamiltonian models, implementing in particular a novel physical realization of a quantum rotor-like Hamiltonian that possesses an anisotropic long range interaction.
The two-dimensional planar spin model in the presence of p-fold random anisotropy has been investigated using Monte Carlo simulation and finite size scaling. The system has been examined for p=2, 3, 4, 5, 6 and lattice sizes N=4 2 , 8 2 , 16 2 . The critical behaviour is found to depend on the value of p and is of two types. For p=3, 5, 6 the results indicate a transition to a quasiferromagnetic state at the same temperature as the pure system. At lower temperatures there is evidence for a second transition; however, the system remains quasiferromagnetic. For p=2, 4 the behaviour is different and results suggest a second-order transition to a spin glass phase and no quasiferromagnetism.
The Berezinskii-Kosterlitz-Thouless (BKT) phase transition in two-dimensional planar rotator and XYXYXY models on a square lattice, diluted by randomly placed vacancies, is studied here using hybrid Monte Carlo simulations that combine single spin flip, cluster, and over-relaxation techniques. The transition temperature Tc{T}_{c}Tc​ is determined as a function of vacancy density ${\ensuremath{\rho}}_{\mathrm{vac}}$ by finite-size scaling of the helicity modulus and the in-plane magnetic susceptibility. The results for Tc{T}_{c}Tc​ are consistent with those from the much less precise fourth-order cumulant of Binder. Tc{T}_{c}Tc​ is found to decrease monotonically with increasing ${\ensuremath{\rho}}_{\mathrm{vac}}$, and falls to zero close to the square lattice percolation limit, ${\ensuremath{\rho}}_{\mathrm{vac}}\ensuremath{\approx}0.41$. The result is physically reasonable: the quasi-long-range orientational order of the low-temperature phase cannot be maintained in the absence of sufficient spin interactions across the lattice.
We study the phase diagram and the quantum phase transitions of a site-diluted two-dimensional O(3) quantum rotor model by means of large-scale Monte Carlo simulations. This system has two quantum phase transitions: a generic one for small dilutions and a percolation transition across the lattice percolation threshold. We determine the critical behavior for both transitions and for the multicritical point that separates them. In contrast to the exotic scaling scenarios found in other random quantum systems, all these transitions are characterized by finite-disorder fixed points with power-law scaling. We relate our findings to a recent classification of phase transitions with quenched disorder according to the rare region dimensionality, and we discuss experiments in disordered quantum magnets.