Orientational phase transitions in the quantum anisotropic planar rotor model

Min-Chul Cha, Ji-Woo Lee

Min-Chul Cha, 이지우

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

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.

Balázs Hetényi, B. J. Berne

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*.

Tobias Serwatka, Pierre–Nicholas Roy

In this work, we perform a density matrix renormalization group study of chains of planar rotors interacting via dipolar interactions. By exploring the ground state from weakly to strongly interacting rotors, we find the occurrence of a quantum phase transition between a disordered and a dipole-ordered quantum state. We show that the nature of the ordered state changes from ferroelectric to antiferroelectric when the relative orientation of the rotor planes varies and that this change requires no modification of the overall symmetry. The observed quantum phase transitions are characterized by critical exponents and central charges, which reveal different universality classes ranging from that of the (1 + 1)D Ising model to the 2D classical XY model.

Jürg Martin Fröhlich, Élliott H. Lieb