arXiv subjects

S. A. Vitiello

Publications and source records attributed to S. A. Vitiello.

17 recordsLinked to original sources

arXiv2025

Neural network-based nodal structures optimization for interacting fermionic systems

Simulating strongly correlated fermionic systems remains a fundamental challenge in quantum physics, largely due to the sign problem in quantum Monte Carlo (QMC) methods. We present a neural network-based variational Monte Carlo (NN-VMC) approach, leveraging a flexible neural network ansatz to represent the many-body wavefunction. Focusing on quantum dots with up to 30 electrons, we demonstrate that NN-VMC significantly reduces variational bias and achieves ground-state energies surpassing those of fixed-node diffusion Monte Carlo (DMC). A key feature is that the neural network adaptively learns and optimizes nodal structures during energy minimization. We provide qualitative insights into the nodal structure of fermionic wavefunctions by comparing the nodal structures generated by NN-VMC with those obtained from traditional trial functions. Additionally, we reveal spin-resolved radial distributions and electron density profiles, highlighting the versatility and accuracy of NN-VMC. This work underscores the potential of machine learning to advance quantum simulations and deepen our understanding of strongly correlated systems.

physics.comp-ph↗

arXiv2023

Synergy between deep neural networks and the variational Monte Carlo method for small $^4He_N$ clusters

We introduce a neural network-based approach for modeling wave functions that satisfy Bose-Einstein statistics. Applying this model to small $^4He_N$ clusters (with N ranging from 2 to 14 atoms), we accurately predict ground state energies, pair density functions, and two-body contact parameters $C^{(N)}_2$ related to weak unitarity. The results obtained via the variational Monte Carlo method exhibit remarkable agreement with previous studies using the diffusion Monte Carlo method, which is considered exact within its statistical uncertainties. This indicates the effectiveness of our neural network approach for investigating many-body systems governed by Bose-Einstein statistics.

physics.atm-clus↗

arXiv2023

Properties of fermionic systems with the Path-integral ground state method

We investigate strongly correlated many-body systems composed of bosons and fermions with a fully quantum treatment using the path-integral ground state method, PIGS. To account for the Fermi-Dirac statistics, we implement the fixed-node approximation into PIGS, which we then call FN-PIGS. In great detail, we discuss the pair density matrices we use to construct the full density operator in coordinate representation, a vital ingredient of the method. We consider the harmonic oscillator as a proof-of-concept and, as a platform representing quantum many-body systems, we explore helium atoms. Pure $^4$He systems demonstrate most of the features of the method. Complementarily, for pure $^3$He, the fixed-node approximation resolves the ubiquitous sign problem stemming from anti-symmetric wave functions. Finally, we investigate $^3$He-$^4$He mixtures, demonstrating the method's robustness. One of the main features of FN-PIGS is its ability to estimate any property at temperature $T=0$ without any additional bias apart from the FN approximation; biases from long simulations are also excluded. In particular, we calculate the correlation function of pairs of equal and opposite spins and precise values of the $^3$He kinetic energy in the mixture.

cond-mat.quant-gas↗

arXiv2021

Finite-range effects in the unitary Fermi polaron

Quantum Monte Carlo techniques are employed to study the properties of polarons in an ultracold Fermi gas, at $T= 0,$ and in the unitary regime using both a zero-range model and a square-well potential. For a fixed density, the potential range is varied and results are extrapolated and compared against a zero-range model. A discussion regarding the choice of an interacting potential with a finite range is presented. We compute the polaron effective mass, the polaron binding energy, and the effective coupling between them. The latter is obtained using the Landau-Pomeranchuk's weakly interacting quasiparticle model. The contact parameter is estimated by fitting the pair distribution function of atoms in different spin states.

cond-mat.quant-gas↗

arXiv2018

Estimated values of the kinetic energy for liquid $^3$He

The kinetic energy is estimated for the ground-state of liquid $^3$He at equilibrium density. The obtained value for this quantity, $10.16\pm0.05$ K/atom at density $0.0163~\mboxÅ$, is in agreement with most of the experimental data found in the literature. This result resolves a long-standing controversy between experimental and theoretical values of this quantity. The variational path integral method, an "exact" quantum Monte Carlo method extended for fermionic systems, is applied in the calculations. The results obtained are subjected only to the restrictions imposed by a chosen nodal structure without any further approximation, even for quantities that do not commute with the Hamiltonian. The required fixed-node approximation entails an implementation that allows a more effective estimation of the quantities of interest. Total and potential energies together with the radial distribution function are also computed.

cond-mat.quant-gas↗

arXiv2017

Ground-state properties of unitary bosons: from clusters to matter

The properties of cold Bose gases at unitarity have been extensively investigated in the last few years both theoretically and experimentally. In this paper we use a family of interactions tuned to two-body unitarity and very weak three-body binding to demonstrate the universal properties of both clusters and matter. We determine the universal properties of finite clusters up to 60 particles and, for the first time, explicitly demonstrate the saturation of energy and density with particle number and compare with bulk properties. At saturation in the bulk we determine the energy, density, two- and three-body contacts and the condensate fraction. We find that uniform matter is more bound than three-body clusters by nearly two orders of magnitude, the two-body contact is very large in absolute terms, and yet the condensate fraction is also very large, greater than 90%. Equilibrium properties of these systems may be experimentally accessible through rapid quenching of weakly-interacting boson superfluids.

cond-mat.quant-gas↗

arXiv2017

Shadow wave function with a symmetric kernel

A shadow wave function with an explicit symmetric kernel is introduced. As a consequence the atoms exchange in the system is enhanced. Basic properties of this class of trial functions are kept and quantities it can describe are easily estimated. The effectiveness of this approach is analized by computing properties of interest in a system formed from 4He atoms.

quant-ph↗

arXiv2015

Contact interaction in an unitary ultracold Fermi gas

An ultracold Fermi atomic gas at unitarity presents universal properties that in the diluted limit can be well described by a contact interaction. By employing a guide function with correct boundary conditions and making simple modifications to the sampling procedure we are able to handle for the first time a true contact interaction in a quantum Monte Carlo calculation. The results are obtained with small variances. Our calculations for the Bertsch and contact parameters are in excellent agreement with published experiments. The possibility of using a more faithfully description of ultracold atomic gases can help uncover features yet unknown of the ultracold atomic gases. In addition, this work paves the way to perform quantum Monte Carlo calculations for systems interacting with contact interactions, where in many cases the description using potentials with finite effective range might not be accurate.

cond-mat.quant-gas↗

arXiv2015

Kinetic energies of liquid and solid phases of $^4$He

Kinetic energies of a system of $^4$He are investigated at zero temperature. The multi-weight extension to the diffusion Monte Carlo method is used to implement the Feynman-Hellmann theorem in an effective way. This method allows the quantities of interest to be computed with excellent accuracy. In order to study the importance of symmetry in the kinetic energy calculations, we have considered for the solid phase two guiding wave functions: the Nosanov-Jastrow without boson symmetry and the symmetric Nosanov-Jastrow with boson symmetry. In general very good agreement is found with the experimental data at both the liquid and solid phases.

cond-mat.other↗

arXiv2014

Monte Carlo calculations for Fermi gases in the unitary limit with a zero-range interaction

An ultracold Fermi gas with a zero-range attractive potential in the unitary limit is investigated using variational and diffusion Monte Carlo methods. Previous calculations have used a finite range interactions and extrapolate the results to zero-range. Here we extend the quantum Monte Carlo method to directly use a zero-range interaction without extrapolation. We employ a trial wave function with the correct boundary conditions, and modify the sampling procedures to handle the zero-range interaction. The results are reliable and have low variance.

cond-mat.quant-gas↗

arXiv2012

Elastic constants and supersolidity in solid hcp 4He

The elastic constants of solid \textit{hcp} $^4$He are investigated in molar volumes ranging from about melting up to approximately 14 MPa. Properties of interest are determined by averages formed from computed values in configurations sampled by Monte Carlo of a model wave function. Deviations from known elastic relations are reported near the density where the supersolid fraction is maximum. The results offer further evidence that the supersolid state is related to elastic constants anomalies and that both are manifestations of a single physical process.

cond-mat.other↗

arXiv2010

Dislocation Mobility in a Quantum Crystal: the Case of Solid 4He

We investigate the structure and mobility of dislocations in hcp 4He crystals. In addition to fully characterizing the five elastic constants of this system, we obtain direct insight into dislocation core structures on the basal plane, which demonstrates a tendency toward dissociation into partial dislocations. Moreover, our results suggest that intrinsic lattice resistance is an essential factor in the mobility of these dislocations. This insight sheds new light on the possible correlation between dislocation mobility and the observed macroscopic behavior of crystalline 4He.

cond-mat.mtrl-sci↗

arXiv2009

Zero-point Divacancy Concentration in the Shadow Wave-Function Model for Solid 4He

We address the issue of interaction between zero-point vacancies in solid 4He as described within the shadow wave-function model. Applying the reversible-work method and taking into account finite-size effects, we obtain a zero-point monovacancy concentration of (2.03 +- 0.02) 10^{-3}, which is slightly higher than the result due to Reatto et al. for the same model. Utilizing the same methodology, we then consider the divacancy, taking into account both the in-plane as well as out-of-plane configurations with respect to the basal plane. We find no significant anisotropy between both conformation. Furthermore, although there is a small binding tendency, the expected divacancy concentration is only ~4-5 times larger than the value expected in the absence of any clustering propensity, 2.5 10^{-5}. This result suggests that, within the employed model description, no vacancy aggregation leading to phase separation is to be expected in the ground state.

cond-mat.other↗

arXiv2008

Influence of Anharmonic Effects on the Zero-point Vacancy Concentration in Solid 4He

We conduct a theoretical study in which we determine the zero-point vacancy concentration in solid 4He at T=0 K. To this end, we employ the quantum-classical isomorphism, by which the quantum-mechanical probability density function of a system composed of bosons at T=0K can be interpreted in terms of a Boltzmann factor of a classical system at finite temperature. By using this classical isomorph we apply the methods of classical statistical mechanics to compute the vacancy formation free energy and the vacancy concentration in the associated quantum system at T=0. In this context, we focus specifically on the role of anharmonic effects that are expected to be non-negligible due to the significant zero-point motion. For this purpose, we compute the formation free energies using both the harmonic approximation (HA) as well as reversible-work (RW) method, in which all anharmonic effects are taken into account. The results suggest that anharmonic effects indeed play a significant role, lowering the classical formation free energy by ~25% and increasing the zero-point vacancy concentration by more than an order of magnitude compared to the HA.

cond-mat.other↗

arXiv2004

Quantum linear mutual information and classical correlations in globally pure bipartite systems

We investigate the correlations of initially separable probability distributions in a globally pure bipartite system with two degrees of freedom for classical and quantum systems. A classical version of the quantum linear mutual information is introduced and the two quantities are compared for a system of oscillators coupled with both linear and non-linear interactions. The classical correlations help to understand how much of the quantum loss of purity are due to intrinsic quantum effects and how much is related to the probabilistic character of the initial states, a characteristic shared by both the classical and quantum pictures. Our examples show that, for initially localized Gaussian states, the classical statistical mutual linear entropy follows its quantum counterpart for short times. For non-Gaussian states the behavior of the classical and quantum measures of information are still qualitatively similar, although the fingerprints of the non-classical nature of the initial state can be observed in their different amplitudes of oscillation.

quant-ph↗

arXiv2003

Analysis of the contributions of three-body potentials in the equation of state of 4He

The effect of three-body interatomic contributions in the equation of state of 4He are investigated. A recent two-body potential together with the Cohen and Murrell (Chem. Phys. Lett. 260, 371 (1996)) three-body potential are applied to describe bulk helium. The triple-dipole dispersion and exchange energies are evaluated subjected only to statistical uncertainties. An extension of the diffusion Monte Carlo method is applied in order to compute very small energies differences. The results show how the three-body contributions affects the ground-state energy, the equilibrium, melting and freezing densities.

physics.chem-ph↗

arXiv2003

Spin-orbit induced backflow in neutron matter with auxiliary field diffusion Monte Carlo

The energy per particle of zero-temperature neutron matter is investigated, with particular emphasis on the role of the $\vec L\cdot\vec S$ interaction. An analysis of the importance of explicit spin--orbit correlations in the description of the system is carried out by the auxiliary field diffusion Monte Carlo method. The improved nodal structure of the guiding function, constructed by explicitly considering these correlations, lowers the energy. The proposed spin--backflow orbitals can conveniently be used also in Green's Function Monte Carlo calculations of light nuclei.

nucl-th↗