In this work, we develop a theoretical description of the collective behavior of interacting dipolar planar rotors by using time independent perturbation theory and a small angle quadratic approximation. The ground state properties for both the ordered and disordered quantum phases of the system are directly calculated and analyzed. Time-independent perturbation theory is shown to be appropriate for the disordered phase. For the ordered phase, we construct a quadratic approximation based on the stable equilibrium configurations of the dipolar ordering; we show that the inclusion of the quartic terms from the expansion of the potential energy are essential to correct the shift in the energy spectrum due to quantization ambiguities. Numerical techniques such as Exact Diagonalization and Density Matrix Renormalization Group are used for the benchmark the quality of both approximations.
In this work, we develop a theoretical description of the collective behavior of interacting dipolar planar rotors by using time independent perturbation theory and a small angle quadratic approximation. The ground state properties for both the ordered and disordered quantum phases of the system are directly calculated and analyzed. Time-independent perturbation theory is shown to be appropriate for the disordered phase. For the ordered phase, we construct a quadratic approximation based on the stable equilibrium configurations of the dipolar ordering; we show that the inclusion of the quartic terms from the expansion of the potential energy are essential to correct the shift in the energy spectrum due to quantization ambiguities. Numerical techniques such as Exact Diagonalization and Density Matrix Renormalization Group are used for the benchmark the quality of both approximations.
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.
We study the ground-state properties of linear chains of dipolar planar rotors hindered by a six-fold on-site potential, a model motivated by water molecules confined in the hexagonal cavities of beryl. Using density matrix renormalization group (DMRG) calculations, we locate the quantum phase transition between the disordered and ferroelectrically ordered phases using the von Neumann entanglement entropy and the Binder ratio of the polarization. A sweep of the six-fold pinning strength shows that increasing hindrance shifts the critical dipolar coupling gc to smaller values. These results suggest that crystal-field hindrance can promote, rather than suppress, dipolar ordering. This work has implications for ferroelectricity and quantum-device tuning in confined molecular rotors
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.
We demonstrate the applicability of the Multi-Layer Multi-Configuration Time-Dependent Hartree (ML-MCTDH) method to the problem of computing ground states of one-dimensional chains of linear rotors with dipolar interactions. Specifically, we successfully obtain energies, entanglement entropies, and orientational correlations that are in agreement with the Density Matrix Renormalization Group (DMRG), which has been previously used for this system. We find that the entropies calculated by ML-MCTDH for larger system sizes contain nonmonotonicity, as expected in the vicinity of a second-order quantum phase transition between ordered and disordered rotor states. We observe that this effect remains when all couplings besides nearest-neighbor are omitted from the Hamiltonian, which suggests that it is not sensitive to the rate of decay of the interactions. In contrast to DMRG, which is tailored to the one-dimensional case, ML-MCTDH (as implemented in the Heidelberg MCTDH package) requires more computational time and memory, although the requirements are still within reach of commodity hardware. The numerical convergence and computational demand of two practical implementations of ML-MCTDH and DMRG are presented in detail for various combinations of system parameters.
We consider quantum phases of tightly confined spin-2 bosons in an external field under the presence of rotationally invariant interactions. Generalizing previous treatments, we show how this system can be mapped onto a quantum rotor model. Within the rotor framework, low-energy excitations about fragmented states, which cannot be accessed within standard Bogoliubov theory, can be obtained. In the spatially extended system in the thermodynamic limit there exists a mean field ground-state degeneracy between a family of nematic states for appropriate interaction parameters. It has been established that quantum fluctuations lift this degeneracy through the mechanism of order by disorder and select either a uniaxial or square-biaxial ground state. On the other hand, in the full quantum treatment of the analogous single-spatial-mode problem with finite-particle number, it is known that, due to symmetry-restoring fluctuations, there is a unique ground state across the entire nematic region of the phase diagram. Within the established rotor framework, we investigate the possible quantum phases under the presence of a quadratic Zeeman field, a problem which has previously received little attention. By investigating wave-function overlaps, we do not find any signatures of the order-by-disorder phenomenon which is present in the continuum case. Motivated by this, we consider an alternative external potential which breaks less symmetry than the quadratic Zeeman field. For this case, we do find the phenomenon of order by disorder in the fully quantum system. This is established within the rotor framework and with exact diagonalization.
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*.