Structural transition, orientational order, and anomalous specific heat in a two-dimensional dimer crystal of core-softened particles.

Systems featuring hard-core-soft-shell repulsive pair potentials can form ordered phases, where particles organize themselves in aggregates with nontrivial geometries. The dimer crystal formed by one such potential, namely, the hard-core plus generalized exponential model of order 4, has been recently investigated, revealing a low-temperature structural phase transition, with the onset of nematic ordering of the dimers. In the present work, we aim to characterize this phase transition via a mean-field theory, by which a detailed analysis of the low-temperature properties of the system is carried out under quadrupole approximation. We determine the transition temperature and identify its order parameter, highlighting the link between the structural transition and the nematic ordering of the system. The first-order character of the transition is established and supported by the Landau expansion of the free energy in powers of the order parameter. The theory is subsequently generalized to take into account lattice vibrations and dimer length fluctuations. Finally, we provide an explanation for the anomalous behavior displayed by the specific heat in the vanishing-temperature limit, which is also supported by Monte Carlo simulations.

Dynamical stochastic simulation of complex electrical behavior in neuromorphic networks of metallic nanojunctions.

Nanostructured Au films fabricated by the assembling of nanoparticles produced in the gas phase have shown properties suitable for neuromorphic computing applications: they are characterized by a non-linear and non-local electrical behavior, featuring switches of the electric resistance whose activation is typically triggered by an applied voltage over a certain threshold. These systems can be considered as complex networks of metallic nanojunctions where thermal effects at the nanoscale cause the continuous rearrangement of regions with low and high electrical resistance. In order to gain a deeper understanding of the electrical properties of this nano granular system, we developed a model based on a large three dimensional regular resistor network with non-linear conduction mechanisms and stochastic updates of conductances. Remarkably, by increasing enough the number of nodes in the network, the features experimentally observed in the electrical conduction properties of nanostructured gold films are qualitatively reproduced in the dynamical behavior of the system. In the activated non-linear conduction regime, our model reproduces also the growing trend, as a function of the subsystem size, of quantities like Mutual and Integrated Information, which have been extracted from the experimental resistance series data via an information theoretic analysis. This indicates that nanostructured Au films (and our model) possess a certain degree of activated interconnection among different areas which, in principle, could be exploited for neuromorphic computing applications.

Low-temperature ordering of the dimer phase of a two-dimensional model of core-softened particles.

Purely pairwise interactions of the core-softened type, i.e., featuring a soft repulsion followed by a hard-core interaction at shorter distance, give rise to nontrivial equilibrium structures entirely different from the standard close packing of spheres. In particular, in a suitable low-temperature region of their phase diagram, such interactions are well known to favor a transition from a fluid to a cluster crystal. The residual mutual interaction between individual clusters can lead to the formation of patterns of their reciprocal orientations. In this work, we investigate two examples of such models in two dimensions, at the density most appropriate to the dimer phase, whereby clusters consist of just two particles, studying them with optimization techniques and Monte Carlo simulations. We focus on the dimer crystal, and unveil a second phase transition at extremely low temperature. This transition leads from a triangular dimer lattice with randomly disordered dimer orientations at high temperature to a reduced-symmetry ground state with nematic orientational order and a slightly distorted structure characterized by a centered-rectangular lattice at low temperature.

Emergence of an Ising critical regime in the clustering of one-dimensional soft matter revealed through string variables.

Soft matter systems are renowned for being able to display complex emerging phenomena such as clustering phases. Recently, a surprising quantum phase transition has been revealed in a one-dimensional (1D) system composed of bosons interacting via a pairwise soft potential in the continuum. It was shown that the spatial coordinates undergoing two-particle clustering could be mapped into quantum spin variables of a 1D transverse Ising model. In this work we investigate the manifestation of an analogous critical phenomenon in 1D classical fluids of soft particles in the continuum. In particular, we study the low-temperature behavior of three different classical models of 1D soft matter, whose interparticle interactions allow for clustering. The same string variables highlight that, at the commensurate density for the two-particle cluster phase, the peculiar pairing of neighboring soft particles can be nontrivially mapped onto a 1D discrete classical Ising model. We also observe a related phenomenon, namely the presence of an anomalous peak in the low-temperature specific heat, thus indicating the emergence of Schottky phenomenology in a nonmagnetic fluid.

One-Dimensional Liquid

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.

Dynamics of charge migration in poly(para-phenylene vinylene) films and nanocomposites with single walled carbon nanotubes.

We present in this paper a comprehensive study of the migration dynamics of the charges underlying transient photoluminescence (PL) processes in poly(para-phenylene vinylene) (PPV) samples from room temperature to 13 K. In order to interpret experimental data, we have modelled the long-time PL decays (from 100 to 1000 ps) using a time function proportional to [Formula: see text] in which the parameter α is evaluated in a Monte Carlo simulation on polymeric chains. The one dimensional chains (2000 sites long) are formed by random sequences of long and short conjugated segments whose bimodal distributions have been elaborated in previous works in order to reproduce the PL band shapes and peak positions. Intra-chain and inter-chain dynamics are taken into account in the migration of the photogenerated charges from short to long conjugated segments. The statistical analysis is performed by averaging over a total of 10(6) trials for each initial conditions. The values of α have been determined for pristine PPV films and PPV composite films with single-walled carbon nanotubes. This theoretical analysis is in good agreement with experimental data and provides a coherent description for the migration of the photogenerated charges in such inhomogeneous polymeric systems.

Imaginary time density-density correlations for two-dimensional electron gases at high density.

We evaluate imaginary time density-density correlation functions for two-dimensional homogeneous electron gases of up to 42 particles in the continuum using the phaseless auxiliary field quantum Monte Carlo method. We use periodic boundary conditions and up to 300 plane waves as basis set elements. We show that such methodology, once equipped with suitable numerical stabilization techniques necessary to deal with exponentials, products, and inversions of large matrices, gives access to the calculation of imaginary time correlation functions for medium-sized systems. We discuss the numerical stabilization techniques and the computational complexity of the methodology and we present the limitations related to the size of the systems on a quantitative basis. We perform the inverse Laplace transform of the obtained density-density correlation functions, assessing the ability of the phaseless auxiliary field quantum Monte Carlo method to evaluate dynamical properties of medium-sized homogeneous fermion systems.

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.

Imaginary time correlations and the phaseless auxiliary field quantum Monte Carlo.

The phaseless Auxiliary Field Quantum Monte Carlo (AFQMC) method provides a well established approximation scheme for accurate calculations of ground state energies of many-fermions systems. Here we address the possibility of calculating imaginary time correlation functions with the phaseless AFQMC. We give a detailed description of the technique and test the quality of the results for static properties and imaginary time correlation functions against exact values for small systems.

Path integral Monte Carlo study of 4He clusters doped with alkali and alkali-earth ions.

Path integral Monte Carlo calculations of (4)He nanodroplets doped with alkali (Na(+), K(+) and Cs(+)) and alkali-earth (Be(+) and Mg(+)) ions are presented. We study the system at T = 1 K and between 14 and 128 (4)He atoms. For all studied systems, we find that the ion is well localized at the center of the droplet with the formation of a "snowball" of well-defined shells of localized (4)He atoms forming solid-like order in at least the first surrounding shell. The number of surrounding helium shells (two or three) and the number of atoms per shell and the degree of localization of the helium atoms are sensitive to the type of ion. The number of (4)He atoms in the first shell varies from 12 for Na(+) to 18 for Mg(+) and depends weakly on the size of the droplet. The study of the density profile and of the angular correlations shows that the local solid-like order is more pronounced for the alkali ions with Na(+) giving a very stable icosahedral order extending up to three shells.

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.

Exact ground state Monte Carlo method for Bosons without importance sampling.

Generally "exact" quantum Monte Carlo computations for the ground state of many bosons make use of importance sampling. The importance sampling is based either on a guiding function or on an initial variational wave function. Here we investigate the need of importance sampling in the case of path integral ground state (PIGS) Monte Carlo. PIGS is based on a discrete imaginary time evolution of an initial wave function with a nonzero overlap with the ground state, which gives rise to a discrete path which is sampled via a Metropolis-like algorithm. In principle the exact ground state is reached in the limit of an infinite imaginary time evolution, but actual computations are based on finite time evolutions and the question is whether such computations give unbiased exact results. We have studied bulk liquid and solid (4)He with PIGS by considering as initial wave function a constant, i.e., the ground state of an ideal Bose gas. This implies that the evolution toward the ground state is driven only by the imaginary time propagator, i.e., there is no importance sampling. For both phases we obtain results converging to those obtained by considering the best available variational wave function (the shadow wave function) as initial wave function. Moreover we obtain the same results even by considering wave functions with the wrong correlations, for instance, a wave function of a strongly localized Einstein crystal for the liquid phase. This convergence is true not only for diagonal properties such as the energy, the radial distribution function, and the static structure factor, but also for off-diagonal ones, such as the one-body density matrix. This robustness of PIGS can be traced back to the fact that the chosen initial wave function acts only at the beginning of the path without affecting the imaginary time propagator. From this analysis we conclude that zero temperature PIGS calculations can be as unbiased as those of finite temperature path integral Monte Carlo. On the other hand, a judicious choice of the initial wave function greatly improves the rate of convergence to the exact results.

Bose-Einstein condensation of incommensurate solid 4He.

It is pointed out that the simulation computation of energy performed so far cannot be used to decide if the ground state of solid 4He has the number of lattice sites equal to the number of atoms (commensurate state) or if it is different (incommensurate state). The best variational wave function, a shadow wave function, gives an incommensurate state, but the equilibrium concentration of vacancies remains to be determined. We have computed the one-body density matrix in solid 4He for the incommensurate state by means of an exact ground state projector method in which incommensurability occurs spontaneously. We find a vacancy induced Bose-Einstein condensation of about 0.23 atoms per vacancy at a pressure of 54 bar. This means that bulk solid 4He is supersolid at low enough temperature if the exact ground state is incommensurate.

Vacancy excitation spectrum in solid 4He and longitudinal phonons.

The first microscopic ab initio calculation of the excitation spectrum of a vacancy in solid 4He is reported. The energy-wave vector dispersion relation has been obtained at melting density within a development of the shadow wave function variational technique. The calculation of the excitation spectrum of a vacancy gives a bandwidth which ranges from 6 to 10 K in the hcp solid 4He, depending on the particular direction of the wave vector of the excitation. The effective mass of the vacancy turns out to be about 0.35 4He masses. We have also computed the spectrum of longitudinal phonons and we find rather good agreement with recent experimental results.