Path Integral Ground State with a Fourth-Order Propagator: Application to Condensed Helium

Ground state properties of condensed Helium are calculated using the Path Integral Ground State (PIGS) method. A fourth-order approximation is used as short (imaginary) time propagator. We compare our results with those obtained with other Quantum Monte Carlo techniques and different propagators. For this particular application, we find that the fourth-order propagator performs comparably to the pair product approximation, and is far superior to the primitive approximation. Results obtained for the equation of state of condensed Helium show that PIGS compares favorably to other QMC methods traditionally utilized for this type of calculation

A molecular superfluid: non-classical rotations in doped para-hydrogen clusters

Clusters of para-hydrogen (pH2) have been predicted to exhibit superfluid behavior, but direct observation of this phenomenon has been elusive. Combining experiments and theoretical simulations, we have determined the size evolution of the superfluid response of pH2 clusters doped with carbon dioxide (CO2). Reduction of the effective inertia is observed when the dopant is surrounded by the pH2 solvent. This marks the onset of molecular superfluidity in pH2. The fractional occupation of solvation rings around CO2 correlates with enhanced superfluid response for certain cluster sizes

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

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

In recent years, experimental techniques have enabled the creation of 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 50 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 towards rotational spectra of such nanomolecular 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.Comment: 5 pages, 4 figure

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

Quantifying entanglement of rotor chains using basis truncation: Application to dipolar endofullerene peapods

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in Halverson, T., Iouchtchenko, D., & Roy, P.-N. (2018). Quantifying entanglement of rotor chains using basis truncation: Application to dipolar endofullerene peapods. Journal of Chemical Physics, 148(7), 074112 and may be found at https://doi.org/10.1063/1.5011769We propose a variational approach for the calculation of the quantum entanglement entropy of assemblies of rotating dipolar molecules. A basis truncation scheme based on the total angular momentum quantum number is proposed. The method is tested on hydrogen fluoride (HF) molecules confined in C60 fullerene cages themselves trapped in a nanotube to form a carbon peapod. The rotational degrees of freedom of the HF molecules and dipolar interactions between neighboring molecules are considered in our model Hamiltonian. Both screened and unscreened dipoles are simulated and results are obtained for the ground state and one excited state that is expected to be accessible via a far-infrared collective excitation. The effect of basis truncation on energetic and entanglement properties is examined and discussed in terms of size extensivity. It is empirically found that for unscreened dipoles, a total angular momentum cutoff that increases linearly with the number of rotors is required in order to obtain proper system size scaling of the chemical potential and entanglement entropy. Recent experiments [A. Krachmalnicoff et al., Nat. Chem. 8, 953 (2016)] suggest substantial screening of the HF dipole moment, so much smaller basis sets are required to obtain converged results in this realistic case. Static correlation functions are also computed and are shown to decay much quicker in the case of screened dipoles. Our variational results are also used to test the accuracy of perturbative and pairwise ansatz treatments.Natural Sciences and Engineering Research Council Ontario Ministry of Research and Innovation Canada Research Chair program Canada Foundation for Innovation Canada First Research Excellence Fun

Reconstructing quantum molecular rotor ground states

Nanomolecular assemblies of C$_{60}$ can be synthesized to enclose dipolar molecules. The low-temperature states of such endofullerenes are described by quantum mechanical rotors, which are candidates for quantum information devices with higher-dimensional local Hilbert spaces. The experimental exploration of endofullerene arrays comes at a time when machine learning techniques are rapidly being adopted to characterize, verify, and reconstruct quantum states from measurement data. In this paper, we develop a strategy for reconstructing the ground state of chains of dipolar rotors using restricted Boltzmann machines (RBMs) adapted to train on data from higher-dimensional Hilbert spaces. We demonstrate accurate generation of energy expectation values from an RBM trained on data in the free-rotor eigenstate basis, and explore the learning resources required for various chain lengths and dipolar interaction strengths. Finally, we show evidence for fundamental limitations in the accuracy achievable by RBMs due to the difficulty in imposing symmetries in the sampling procedure. We discuss possible avenues to overcome this limitation in the future, including the further development of autoregressive models such as recurrent neural networks for the purposes of quantum state reconstruction.Comment: 11 pages, 7 figure

A path integral ground state replica trick approach for the computation of entanglement entropy of dipolar linear rotors

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in J. Chem. Phys. 152, 184113 (2020) and may be found at https://doi.org/10.1063/5.0004602.We calculate the second Rényi entanglement entropy for systems of interacting linear rotors in their ground state as a measure of entanglement for continuous rotational degrees of freedom. The entropy is defined in relation to the purity of a subsystem in a bipartite quantum system, and to compute it, we compare two sampling ensembles based on the path integral ground state (PIGS) formalism. This scheme centers on the replica trick and is aided by the ratio trick, both developed in this context by Hastings et al. [Phys. Rev. Lett. 104, 157201 (2010)]. We study a system composed of linear quantum rotors on a lattice in one dimension, interacting via an anisotropic dipole–dipole potential. The ground state second Rényi entropies estimated by PIGS are benchmarked against those from the density matrix renormalization group for various interaction strengths and system sizes. We find that the entropy grows with an increase in interaction strength, and for large enough systems, it appears to plateau near log(2). We posit that the limiting case of many strongly interacting rotors behaves akin to a lattice of two-level particles in a cat state, in which one naturally finds an entanglement entropy of log(2).Natural Sciences and Engineering Research Council (NSERC), Grant RGPIN-2016-04403 || Ontario Ministry of Research and Innovation (MRI) || Canada Research Chair program, Grant 950-231024 || Canada Foundation for Innovation (CFI), Grant 35232 || Compute Canada || Canada First Research Excellence Fund (CFREF