Exact ground state Monte Carlo method for Bosons without importance sampling

Absence of Off-Diagonal Long-Range Order in hcp ^{4}He Dislocation Cores

The mass transport properties along dislocation cores in hcp ^{4}He are revisited by considering two types of edge dislocations as well as a screw dislocation, using a fully correlated quantum simulation approach. Specifically, we employ the zero-temperature path-integral ground state (PIGS) method together with ergodic sampling of the permutation space to investigate the fundamental dislocation core structures and their off-diagonal long-range order properties. It is found that the Bose-Einstein condensate fraction of such defective ^{4}He systems is practically null (≤10^{-6}), just as in the bulk defect-free crystal. These results provide compelling evidence for the absence of intrinsic superfluidity in dislocation cores in hcp ^{4}He and challenge the superfluid dislocation-network interpretation of the mass-flux-experiment observations, calling for further experimental investigation.

Quantum Symmetry from Enhanced Sampling Methods

We address the problem of the minus sign sampling for two-electron systems using the path integral approach. We show that this problem can be reexpressed as one of computing free energy differences and sampling the tails of statistical distributions. Using metadynamics, a realistic problem like that of two electrons confined in a quantum dot can be solved. We believe that this is a strategy that can possibly be extended to more complex systems.

Probing Quantum Turbulence in ^{4}He by Quantum Evaporation Measurements

Theory of superfluid ^{4}He shows that, due to strong correlations and backflow effects, the density profile of a vortex line has the character of a density modulation and it is not a simple rarefaction region as found in clouds of cold bosonic atoms. We find that the basic features of this density modulation are represented by a wave packet of cylindrical symmetry in which rotons with a positive group velocity have a dominant role: The vortex density modulation can be viewed as a cloud of virtual excitations, mainly rotons, sustained by the phase of the vortex wave function. This suggests that in a vortex reconnection some of these rotons become real so that a vortex tangle is predicted to be a source of nonthermal rotons. The presence of such vorticity induced rotons can be verified by measurements at low temperature of quantum evaporation of ^{4}He atoms. We estimate the rate of evaporation and this turns out to be detectable by current instrumentation. Additional information on the microscopic processes in the decay of quantum turbulence will be obtained if quantum evaporation by high energy phonons should be detected.

Metal-Insulator Transition of Solid Hydrogen by the Antisymmetric Shadow Wave Function

We revisit the pressure-induced molecular-atomic metal-insulator transition of solid hydrogen by means of variational quantum Monte Carlo simulations based on the antisymmetric shadow wave function. For the purpose of facilitating the study of the electronic structure of large-scale fermionic systems, the shadow wave function formalism is extended by a series of technical advancements as implemented in our HswfQMC code. Among others, these improvements include a revised optimization method for the employed shadow wave function and an enhanced treatment of periodic systems with long-range interactions. It is found that the superior accuracy of the antisymmetric shadow wave function results in a significantly increased transition pressure with respect to previous theoretical estimates.

Nonlinear Network Description for Many-Body Quantum Systems in Continuous Space

We show that the recently introduced iterative backflow wave function can be interpreted as a general neural network in continuum space with nonlinear functions in the hidden units. Using this wave function in variational Monte Carlo simulations of liquid ^{4}He in two and three dimensions, we typically find a tenfold increase in accuracy over currently used wave functions. Furthermore, subsequent stages of the iteration procedure define a set of increasingly good wave functions, each with its own variational energy and variance of the local energy: extrapolation to zero variance gives energies in close agreement with the exact values. For two dimensional ^{4}He, we also show that the iterative backflow wave function can describe both the liquid and the solid phase with the same functional form-a feature shared with the shadow wave function, but now joined by much higher accuracy. We also achieve significant progress for liquid ^{3}He in three dimensions, improving previous variational and fixed-node energies.

Quantum Critical Behavior of One-Dimensional Soft Bosons in the Continuum

We consider a zero-temperature one-dimensional system of bosons interacting via the soft-shoulder potential in the continuum, typical of dressed Rydberg gases. We employ quantum Monte Carlo simulations, which allow for the exact calculation of imaginary-time correlations, and a stochastic analytic continuation method, to extract the dynamical structure factor. At finite densities, in the weakly interacting homogeneous regime, a rotonic spectrum marks the tendency to clustering. With strong interactions, we indeed observe cluster liquid phases emerging, characterized by the spectrum of a composite harmonic chain. Luttinger theory has to be adapted by changing the reference lattice density field. In both the liquid and cluster liquid phases, we find convincing evidence of a secondary mode, which becomes gapless only at the transition. In that region, we also measure the central charge and observe its increase towards c=3/2, as recently evaluated in a related extended Bose-Hubbard model, and we note a fast reduction of the Luttinger parameter. For two-particle clusters, we then interpret such observations in terms of the compresence of a Luttinger liquid and a critical transverse Ising model, related to the instability of the reference lattice density field towards coalescence of sites, typical of potentials which are flat at short distances. Even in the absence of a true lattice, we are able to evaluate the spatial correlation function of a suitable pseudospin operator, which manifests ferromagnetic order in the cluster liquid phase, exponential decay in the liquid phase, and algebraic order at criticality.

Weakly parametrized Jastrow ansatz for a strongly correlated Bose system

We consider the Jastrow pair-product wavefunction for strongly correlated Bose systems, in our case liquid helium-4. An ansatz is proposed for the pair factors which consist of a numeric solution to a modified and parametrized pair scattering equation. We consider a number of such simple one-variable parametrizations. Additionally, we allow for a parametrizeable cutoff of the pair factors and for the addition of a long-range phonon tail. This approach results in many-body wavefunctions that have between just one and three variational parameters. Calculation of observables is carried with the variational Monte Carlo method. We find that such a simple parametrization is sufficient to produce results that are comparable in quality to the best available two-body factors for helium. For the two-parameter wavefunction, we find variational energies of -6.04 K per particle for a system of one thousand particles. It is also shown that short-range two-body correlations are reproduced in good detail by the two- and three-parameter functions.

One-Dimensional Liquid ^{4}He: Dynamical Properties beyond Luttinger-Liquid Theory

We compute the zero-temperature dynamical structure factor of one-dimensional liquid ^{4}He by means of state-of-the-art quantum Monte Carlo and analytic continuation techniques. By increasing the density, the dynamical structure factor reveals a transition from a highly compressible critical liquid to a quasisolid regime. In the low-energy limit, the dynamical structure factor can be described by the quantum hydrodynamic Luttinger-liquid theory, with a Luttinger parameter spanning all possible values by increasing the density. At higher energies, our approach provides quantitative results beyond the Luttinger-liquid theory. In particular, as the density increases, the interplay between dimensionality and interaction makes the dynamical structure factor manifest a pseudo-particle-hole continuum typical of fermionic systems. At the low-energy boundary of such a region and moderate densities, we find consistency, within statistical uncertainties, with predictions of a power-law structure by the recently developed nonlinear Luttinger-liquid theory. In the quasisolid regime, we observe a novel behavior at intermediate momenta, which can be described by new analytical relations that we derive for the hard-rods model.

Mixing effects in the crystallization of supercooled quantum binary liquids

By means of Raman spectroscopy of liquid microjets, we have investigated the crystallization process of supercooled quantum liquid mixtures composed of parahydrogen (pH2) or orthodeuterium (oD2) diluted with small amounts of neon. We show that the introduction of the Ne impurities affects the crystallization kinetics in terms of a significant reduction of the measured pH2 and oD2 crystal growth rates, similarly to what found in our previous work on supercooled pH2-oD2 liquid mixtures [Kühnel et al., Phys. Rev. B 89, 180201(R) (2014)]. Our experimental results, in combination with path-integral simulations of the supercooled liquid mixtures, suggest in particular a correlation between the measured growth rates and the ratio of the effective particle sizes originating from quantum delocalization effects. We further show that the crystalline structure of the mixtures is also affected to a large extent by the presence of the Ne impurities, which likely initiate the freezing process through the formation of Ne-rich crystallites.

Population size bias in diffusion Monte Carlo

The size of the population of random walkers required to obtain converged estimates in diffusion Monte Carlo (DMC) increases dramatically with system size. We illustrate this by comparing ground state energies of small clusters of parahydrogen (up to 48 molecules) computed by DMC and path integral ground state (PIGS) techniques. We contend that the bias associated with a finite population of walkers is the most likely cause of quantitative numerical discrepancies between PIGS and DMC energy estimates reported in the literature, for this few-body Bose system. We discuss the viability of DMC as a general-purpose ground state technique, and argue that PIGS, and even finite temperature methods, enjoy more favorable scaling, and are therefore a superior option for systems of large size.

Higher order diffusion Monte Carlo propagators for linear rotors as diffusion on a sphere: development and application to O2@He(n)

Exploiting the theoretical treatment of particles diffusing on corrugated surfaces and the isomorphism between the "particle on a sphere" and a linear molecule rotation, a new diffusion kernel is introduced to increase the order of diffusion Monte Carlo (DMC) simulations involving linear rotors. Tests carried out on model systems indicate the superior performances of the new rotational diffusion kernel with respect to the simpler alternatives previously employed. In particular, it is evidenced a second order convergence toward exact results with respect to the time step of dynamical correlation functions, a fact that guarantees an identical order for the diffusion part of the DMC projector. The algorithmic advantages afforded by the latter are discussed, especially with respect to the "a posteriori" and "on the fly" extrapolation schemes. As a first application to the new algorithm, the structure and energetics of O(2)@He(n) (n = 1-40) clusters have been studied. This was done to investigate the possible cause of the quenching of the reaction between O(2) and Mg witnessed upon increasing the size of superfluid He droplets used as a solvent. With the simulations on O(2) indicating a strong localization in the cluster core, the behaviour as a function of n is ascribed to the extremely fluxional comportment of Mg@He(n), which dwells far from the droplet center, albeit being solvated, when n is large.

Quantum dislocations: the fate of multiple vacancies in two-dimensional solid 4He

Defects are believed to play a fundamental role in the supersolid state of (4)He. We have studied solid (4)He in two dimensions (2D) as a function of the number of vacancies n(v), up to 30, inserted in the initial configuration at ρ=0.0765 Å( - 2), close to the melting density, with the exact zero-temperature shadow path integral ground state method. The crystalline order is found to be stable also in the presence of many vacancies and we observe two completely different regimes. For small n(v), up to about 6, vacancies form a bound state and cause a decrease of the crystalline order. At larger n(v), the formation energy of an extra vacancy at fixed density decreases by one order of magnitude to about 0.6 K. It is no longer possible to recognize vacancies in the equilibrated state because they mainly transform into quantum dislocations and crystalline order is found almost independently of how many vacancies have been inserted in the initial configuration. The one-body density matrix in this latter regime shows a non-decaying large distance tail: dislocations, that in 2D are point defects, turn out to be mobile, their number is fluctuating, and they are able to induce exchanges of particles across the system mainly triggered by the dislocation cores. These results indicate that the notion of the incommensurate versus the commensurate state loses meaning for solid (4)He in 2D, because the number of lattice sites becomes ill defined when the system is not commensurate. Crystalline order is found to be stable also in 3D in the presence of up to 100 vacancies.