arXiv subjects

Pierre-Nicholas Roy

Publications and source records attributed to Pierre-Nicholas Roy.

At least 19 recordsLinked to original sources

arXiv2026

Quantum critical behavior in chains of hindered dipolar planar rotors

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

cond-mat.mes-hall↗

arXiv2026

Quantum phases in endofullerene zigzag chains

We employ large-scale density matrix renormalization group calculations to study the quantum phases of dipolar molecules confined in bent (zigzag) endofullerene chains, as a function of the chain angle $\gamma$. For LiF, ferroelectric order persists across the full range $60^\circ < \gamma 180^\circ$, with the critical effective dipole moment increasing as the chain bends and parallel alignment becomes less favorable. Near the equilateral configuration ($\gamma = 60^\circ$), geometric frustration drives a transition to an antiferroelectric N\'eel-ordered phase in which neighboring dipoles anti-align along the chain axis. We show that capturing this reorientation requires including dipolar couplings beyond the nearest-neighbor approximation, since next-nearest-neighbor interactions become equally strong at $\gamma = 60^\circ$. For confined water, o-D$_2$O reproduces both ordered phases, whereas p-H$_2$O -- owing to its large rotational constants -- develops no order at any chain angle despite the enhanced coordination of the bent geometry. Because a zigzag chain is the narrowest stripe of a two-dimensional lattice, these results suggest that engineered endofullerene layers could host a rich variety of dipole-ordered quantum phases beyond the ferroelectric ordering observed in previous work.

physics.chem-ph↗

arXiv2026

Effective theory of quantum phases in the dipolar planar rotor chain

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.

physics.chem-ph↗

arXiv2025

Qubit encodings for lattices of dipolar planar rotors

Near term quantum devices have recently garnered significant interest as promising candidates for investigating difficult-to-probe regimes in many-body physics. To this end, various qubit encoding schemes targeting second quantized Hamiltonians have been proposed and optimized. In this work, we investigate two qubit representations of the planar rotor lattice Hamiltonian. The first representation is realized by decomposing the rotor Hamiltonian projectors in binary and mapping them to spin-1/2 projectors. The second approach relies on embedding the planar rotor lattice Hilbert space in a larger space and recovering the relevant qubit encoded system as a quotient space projecting down to the physical degrees of freedom. This is typically called the unary mapping and is used for bosonic systems. We establish the veracity of the two encoding approaches using sparse diagonalization on small chains and discuss quantum phase estimation resource requirements to simulate small planar rotor lattices on near-term quantum devices.

quant-ph↗

arXiv2025

Path Integral Monte Carlo in the Angular Momentum Basis for a Chain of Planar Rotors

We introduce a Path Integral Monte Carlo (PIMC) 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 (PIGS) method. We propose a Bond-Hamiltonian decomposition for the high temperature density matrix factorization of the imaginary time propagator. We show that \textit{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 (DMRG) 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.

physics.chem-ph↗

arXiv2025

A neural network-based four-body potential energy surface for parahydrogen

We present an isotropic ab initio (para-H$_2$)$_4$ four-body interaction potential energy surface (PES). The electronic structure calculations are performed at the correlated coupled-cluster theory level, with single, double, and perturbative triple excitations. They use an atom-centred augmented correlation-consistent double zeta basis set, supplemented by a $(3s3p2d)$ midbond function. We use a multilayer perceptron to construct the PES. We apply a rescaling transformation to the output energies during training to improve the prediction of weaker energies in the sample data. At long distances, the interaction energies are adjusted to match the empirically-derived four-body dispersion interaction. The four-body interaction energy at short intermolecular separations is net repulsive. The use of this four-body PES, in combination with a first principles pair potential for para-H$_2$ [J. Chem. Phys. 119, 12551 (2015)], and an isotropic ab initio three-body potential for para-H$_2$ [J. Chem. Phys. 156, 044301 (2022)], is expected to provide closer agreement with experimental results.

physics.chem-ph↗

arXiv2025

Path-integral Monte Carlo simulations of solid parahydrogen using two-body, three-body, and four-body ab initio interaction potential energy surfaces

We present path integral Monte Carlo simulation results for the equation of state of solid parahydrogen between $ 0.024 \, {\r{A}}^{-3} $ and $ 0.1 \, {\r{A}}^{-3} $ at $ T = 4.2 \, $ K. The simulations are performed using non-additive isotropic ab initio two-body, three-body, and four-body potential energy surfaces (PES). We apply corrections to account for both the finite size simulation errors and the Trotter factorization errors. Simulations that use only the two-body PES during sampling yield an equation of state similar to that of simulations that use both the two-body and three-body PESs during sampling. With the four-body interaction energy, we predict an equilibrium density of $ 0.02608 \, {\r{A}}^{-3} $, very close to the experimental result of $ 0.0261 \, {\r{A}}^{-3} $. The inclusion of the four-body interaction energy also brings the simulation results in excellent agreement with the experimental pressure-density data until around $ 0.065 \, {\r{A}}^{-3} $, beyond which the simulation results overestimate the pressure. These PESs overestimate the average kinetic energy per molecule at the equilibrium density by about $ 7 \% $ compared to the experimental result. Our findings suggest that, at higher densities, we require five-body and higher-order many-body interactions to quantitatively improve the agreement between the pressure-density curve produced by simulations, and that of experiment. Using the four-body PES during sampling at excessively high densities, where such higher-order many-body interactions are likely to be significant, causes an artificial symmetry breaking in the hcp lattice structure of the solid.

physics.chem-ph↗

arXiv2025

Three-body potential energy surface for parahydrogen

We present a 3D isotropic ab initio three-body (para-H$_2$)$_3$ interaction potential energy surface (PES). The electronic structure calculations are carried out at the correlated coupled-cluster theory level, with single, double, and perturbative triple excitations. The calculations use an augmented correlation-consistent triple zeta basis set and a supplementary midbond function. We construct the PES using the Reproducing-Kernel Hilbert Space toolkit [J. Chem. Inf. Model. 57, 1923 (2017)] with phenomenological and empirical adjustments to account for short-range and long-range behaviour. The (para-H$_2$)$_3$ interaction energies deviate drastically from the Axilrod-Teller-Muto (ATM) potential at short intermolecular separations. We find that the configuration of three para-H$_2$ molecules at the corners of an equilateral triangle is responsible for the majority of the (para-H$_2$)$_3$ interaction energy contribution in a hexagonal-close-packed lattice. In cases where two para-H$_2$ molecules are close to one another while the third is far away, the (para-H$_2$)$_3$ interaction PES takes the form of a modified version of the ATM potential. We expect the combination of this PES together with a first principles para-H$_2$--para-H$_2$ Adiabatic Hindered Rotor potential to outperform a widely-used effective pair potential for condensed many-body systems of para-H$_2$.

physics.chem-ph↗

arXiv2025

Equation of state of solid parahydrogen using ab initio two-body and three-body interaction potentials

We present the equation of state (EOS) of solid parahydrogen between $ 0.024 \, {\r{A}}^{-3} $ and $ 0.1 \, {\r{A}}^{-3} $ at $ T = 4.2 $ K, calculated using path-integral Monte Carlo simulations, with ab initio two-body and three-body interaction potentials. We correct for finite size simulation errors using potential tail corrections. Trotter factorization errors are accounted for, either via extrapolation, or by using a suitably small imaginary time step. We incorporate the three-body interaction using two methods; the full inclusion method, where pair and three-body interactions are used in both Monte Carlo sampling and in the energy estimators, and the perturbative method, where three-body interactions are omitted from sampling but are still present in energy estimations. Both treatments of the three-body interaction return very similar total energies and pressures. The presence of three-body interactions has only minor effects on the structural properties of the solid. Whereas the pair interaction, on its own, significantly overestimates the pressure of solid parahydrogen, the additional presence of the three-body interaction causes a severe underestimation of the pressure. Our findings suggest that accurate simulations of solid parahydrogen require four-body and possibly higher-order many-body interactions. It may also be the case that static interaction potentials are entirely unsuitable for simulations of solid parahydrogen at high densities.

physics.chem-ph↗

arXiv2025

Equation of State and First Principles Prediction of the Vibrational Matrix Shift of Solid Parahydrogen

We generate the equation of state (EOS) of solid parahydrogen using a path-integral Monte Carlo (PIMC) simulation based on a highly accurate first-principles adiabatic hindered rotor (AHR) potential energy curve for the parahydrogen dimer. The EOS curves for the fcc and hcp structures of solid parahydrogen near the equilibrium density show that the hcp structure is the more stable of the two, in agreement with experiment. To accurately reproduce the structural and energy properties of solid parahydrogen, we eliminated by extrapolation the systematic errors associated with the choice of simulation parameters used in the PIMC calculation. We also investigate the temperature dependence of the EOS curves, and the invariance of the equilibrium density with temperature is satisfyingly reproduced. The pressure as a function of density, and the compressibility as a function of pressure, are both calculated using the obtained EOS and are compared with previous simulation results and experiments. We also report the first ever a priori prediction of a vibrational matrix shift from first-principles two-body potential functions, and its result for the equilibrium state agrees well with experiment.

physics.chem-ph↗

arXiv2024

Pair Approximating the Action For Molecular Rotations in Path Integral Monte Carlo

Typical path integral Monte Carlo approaches use the primitive approximation to compute the probability density for a given path. In this work, we develop the pair Discrete Variable Representation (pair-DVR) approach to study molecular rotations. The pair propagator, which was initially introduced to study superfluidity in condensed Helium, is naturally well-suited for systems interacting with a pair-wise potential. Consequently, paths sampled using the pair action tend to be closer to the exact paths (compared to primitive Trotter paths) for such systems leading to convergence with less imaginary time steps. Therefore, our approach relies on using the pair factorization approach in conjunction with a discretized Path Integral Ground State (PIGS) paradigm to study a chain of planar rotors interacting with a pair-wise dipole interaction. We first use the Wigner-Kirkwood density expansion to analyze the asymptotics of the pair propagator in imaginary time. Then, we exhibit the utility of the pair factorization scheme via convergence studies comparing the pair and primitive propagators. Finally, we compute energetic and structural properties of this system including the correlation function and Binder ratio as functions of the coupling strength to examine the behaviour of the pair-DVR method near criticality. Density Matrix Renormalization Group results are used for benchmarking throughout.

physics.chem-ph↗

arXiv2024

Path integral Monte Carlo in a discrete variable representation with Gibbs sampling: dipolar planar rotor chain

In this work, we propose a Path Integral Monte Carlo (PIMC) approach based on discretized continuous degrees of freedom and rejection-free Gibbs sampling. The ground state properties of a chain of planar rotors with dipole-dipole interactions are used to illustrate the approach. Energetic and structural properties are computed and compared to exact diagonalization and Numerical Matrix Multiplication for $N \leq 3$ to assess the systematic Trotter factorization error convergence. For larger chains with up to N = 100 rotors, Density Matrix Renormalization Group (DMRG) calculations are used as a benchmark. We show that using Gibbs sampling is advantageous compared to traditional Metroplolis-Hastings rejection importance sampling. Indeed, Gibbs sampling leads to lower variance and correlation in the computed observables.

physics.chem-ph↗

arXiv2024

Quantum criticality in chains of planar rotors with dipolar interactions

In this contribution 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.

physics.chem-ph↗

arXiv2023

Quantum Criticality and Universal Behavior in Molecular Dipolar Lattices of Endofullerenes

Fullerene cages allow the confinement of single molecules and the construction of molecular assemblies whose properties strongly deviate 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 H2O) 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 by either changing the effective electric dipole moment or by isotopic substitution. In the ordered phase, all systems under consideration are characterized by a universal behavior that only depends on the ratio of the effective electric dipole divided by the rotational constant. A phase diagram is derived and further molecules are proposed as candidates for dipole-ordered endofullerene chains.

cond-mat.mes-hall↗

arXiv2023

Optimized basis sets for DMRG calculations of quantum chains of rotating water molecules

In this contribution, we employ a density matrix based optimization procedure to obtain customized basis functions to describe chains of rotating water molecules in interaction regimes associated with different intermolecular distances. This procedure is shown to yield a very compact basis with a clear truncation criterion based on the population of the single particle basis functions. For the water trimer, we discuss the convergence behavior of several properties and show it to be superior when compared to an energy-based truncated basis. It is demonstrated that the optimized basis reduces the necessary number of basis functions by at least an order of magnitude. Finally, the optimization procedure is employed to study larger chains of up to ten water molecules. The formation of hydrogen bonds as well as its impact on the net polarization of the chain is discussed.

physics.chem-ph↗

arXiv2022

A quantum phase transition in the one-dimensional water chain

The concept of quantum phase transitions (QPT) plays a central role in the description of condensed matter systems. In this contribution, we perform high-quality wavefunction-based simulations to demonstrate the existence of a quantum phase transition in a crucially relevant molecular system, namely water, forming linear chains of rotating molecules. We determine various critical exponents and reveal the water chain QPT to belong to the (1+1) dimensional Ising universality class. Furthermore, the effect of breaking symmetries is examined and it is shown that by breaking the inversion symmetry, the ground state degeneracy of the ordered quantum phase is lifted to yield two many-body states with opposite polarization. The possibility of forming ferroelectric phases together with a thermal stability of the quantum critical regime up to ~10 K makes the linear water chain a promising candidate as a platform for quantum devices.

quant-ph↗

arXiv2021

On the quantum mechanical potential of mean force. I. A path integral perspective

We derive two path integral estimators for the derivative of the quantum mechanical potential of mean force (PMF), which may be numerically integrated to yield the PMF. For the first estimator, we perform the differentiation on the exact path integral, and for the second, we perform the differentiation on the path integral after discretization. These estimators are successfully validated against reference results for the harmonic oscillator and Lennard-Jones dimer systems using constrained path integral Monte Carlo (PIMC) simulations. Specifically, the estimators reproduce both the derivative of the PMF, as well as the PMF itself, for the model systems at multiple temperatures. In Paper II, these estimators are implemented alongside path integral molecular dynamics (PIMD) with a constrained path integral Langevin equation thermostat for use with more general systems and potentials.

physics.chem-ph↗

arXiv2021

On the quantum mechanical potential of mean force. II. Constrained path integral molecular dynamics integrators

Building on Paper I of this series, which introduced path integral Monte Carlo (PIMC) estimators for the derivative of the potential of mean force (PMF), we propose two path integral molecular dynamics (PIMD) integrators that can make use of these estimators. These integrators, c-OBABO and c-BAOAB, are based on the path integral Langevin equation (PILE) integrator, which has seen widespread success in PIMD applications, but they include support for holonomic constraints. When the reaction coordinate is the distance between two centers of mass, we find that several exact expressions are accessible: the Fixman correction, the position constraint Lagrange multiplier, and various derivatives with respect to the reaction coordinate. It is observed that c-BAOAB tends to have a smaller time step error than c-OBABO, which is consistent with previous studies on integrator step ordering in molecular dynamics with holonomic constraints and in PIMD. Further, we show that both the PMF of a water dimer and its derivative may be obtained from PIMD simulations using c-BAOAB, yielding results in agreement with the path integral umbrella sampling method previously used for this system.

physics.chem-ph↗