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arXiv:1805.05420 · The Journal of Chemical Physics

Ground states of linear rotor chains via the density matrix renormalization group

Dmitri Iouchtchenko, Pierre–Nicholas Roy

Published Apr 4, 2018• 23 citations
arXivHTMLPDF

Abstract

In recent years, experimental techniques have enabled the creation of ultracold optical lattices of molecules and endofullerene peapod nanomolecular assemblies. It was previously suggested that the rotor model resulting from the placement of dipolar linear rotors in one-dimensional lattices at low temperature has a transition between ordered and disordered phases. We use the density matrix renormalization group (DMRG) to compute ground states of chains of up to 100 rotors and provide further evidence of the phase transition in the form of a diverging entanglement entropy. We also propose two methods and present some first steps toward rotational spectra of such molecular assemblies using DMRG. The present work showcases the power of DMRG in this new context of interacting molecular rotors and opens the door to the study of fundamental questions regarding criticality in systems with continuous degrees of freedom.

DOI
10.1063/1.5024403

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In recent years, experimental techniques have enabled the creation of ultracold optical lattices of molecules and endofullerene peapod nanomolecular assemblies. It was previously suggested that the rotor model resulting from the placement of dipolar linear rotors in one-dimensional lattices at low temperature has a transition between ordered and disordered phases. We use the density matrix renormalization group (DMRG) to compute ground states of chains of up to 100 rotors and provide further evidence of the phase transition in the form of a diverging entanglement entropy. We also propose two methods and present some first steps toward rotational spectra of such molecular assemblies using DMRG. The present work showcases the power of DMRG in this new context of interacting molecular rotors and opens the door to the study of fundamental questions regarding criticality in systems with continuous degrees of freedom.
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.
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 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
The density matrix renormalization group (DMRG) method generates the low-energy states of linear systems of NNN sites with a few degrees of freedom at each site by starting with a small system and adding sites step by step while keeping constant the dimension of the truncated Hilbert space. DMRG algorithms are adapted to open chains with inversion symmetry at the central site, to cyclic chains and to weakly coupled chains. Physical properties rather than energy accuracy is the motivation. The algorithms are applied to the edge states of linear Heisenberg antiferromagnets with spin S≥1S \ge 1S≥1 and to the quantum phases of a frustrated spin-1/2 chain with exchange between first and second neighbors. The algorithms are found to be accurate for extended Hubbard and related 1D models with charge and spin degrees of freedom.
Fullerene cages allow the confinement of single molecules and the construction of molecular assemblies whose properties strongly differ from those of free species. In this work, we employ the density-matrix renormalization group method to show that chains of fullerenes filled with polar molecules (LiF, HF, and H 2 O) can form dipole-ordered quantum phases. In symmetry broken environments, these ordered phases are ferroelectric, a property that makes them promising candidates for quantum devices. We demonstrate that for a given guest molecule, the occurrence of these quantum phases can be enforced or influenced either by changing the effective electric dipole moment or by isotopic substitution. In the ordered phase, all systems under consideration are characterized by universal behavior that depends only on the ratio of the effective electric dipole and of the rotational constant. A phase diagram is derived, and further molecules are proposed as candidates for dipole-ordered endofullerene chains.
This thesis describes several novel approaches in quantum molecular dynamics for obtaining properties of molecular systems in different regimes. We investigate ground state properties of chains of linear rotors with dipole–dipole interactions via the density matrix renormalization group (DMRG), by deriving the appropriate form of the interaction operator and implementing it in ITensor. This provides us with further evidence of a quantum phase transition in this system. We also improve the sampling of Gaussian mixture distributions for finite temperature path integral Monte Carlo (PIMC) of vibronic Hamiltonians. To do this, we replace random sampling by quasi-random sampling, and improve sampling distributions by optimizing their parameters. Finally, we introduce estimators and integrators for constrained free energy simulations in path integral molecular dynamics (PIMD). This method is applied to the study of a water dimer, for which we obtain a quantum potential of mean force.