arXiv subjects

Saverio Moroni

Publications and source records attributed to Saverio Moroni.

At least 19 recordsLinked to original sources

arXiv2026

Variance reduction for forces and pressure in variational Monte Carlo

We present simple and practical strategies to reduce the variance of Monte Carlo estimators. Our focus is on variational Monte Carlo calculations of atomic forces and pressure in electronic systems, although we show that the underlying ideas apply more broadly to other observables, like pair-correlation and angular-distribution functions, and other methods, including molecular dynamics. For Pulay-type contributions, we show that a minor modification based on the Metropolis acceptance ratio softens the power-law divergence of the variance to a logarithmic one, and that inexpensive regularizations can further suppress outliers at the price of a controlled small bias. For Hellmann-Feynman forces, we derive compact variance-reduced estimators for periodic systems that are straightforward to implement in standard Monte Carlo codes. The approach is illustrated for high-pressure metallic hydrogen with more than a hundred atoms described by neural quantum states, including an application to molecular dynamics driven by the improved forces.

cond-mat.str-el↗

arXiv2025

Optimizing excited states in quantum Monte Carlo: A reassessment of double excitations

Quantum Monte Carlo (QMC) methods have proven to be highly accurate for computing excited states, but the choice of optimization strategies for multiple states remains an active topic of investigation. In this work, we revisit the calculation of double excitation energies in nitroxyl, glyoxal, tetrazine, and cyclopentadienone, exploring different objective functionals and their impact on the accuracy and robustness of QMC. A previous study for these systems employed a penalty functional to enforce orthogonality among the states, but the chosen prefactors did not strictly ensure convergence to the target states. Here, we confirm the reliability of previous results by comparing excitation energies obtained with different functionals and analyzing their consistency. Additionally, we investigate the performance of different functionals when starting from a pre-collapsed excited state, providing insight into their ability to recover the target wave functions.

physics.comp-ph↗

arXiv2025

Neural Wave Functions for High-Pressure Atomic Hydrogen

We leverage the power of neural quantum states to describe the ground state wave function of solid and liquid atomic hydrogen, including both electronic and protonic degrees of freedom. For static protons, the resulting Born-Oppenheimer energies are consistently comparable to or lower than all previous projector Monte Carlo results for systems containing up to $128$ hydrogen atoms. The same level of accuracy is preserved upon inclusion of nuclear quantum effects, thus going beyond the Born-Oppenheimer approximation. In addition, our description overcomes major limitations of current wave functions, notably by avoiding any explicit symmetry assumption on the expected quantum crystal, and sidestepping efficiency issues of imaginary time evolution with disparate mass scales. As a first application, we examine crystal formation in an extremely high-density region up to pressure-induced melting.

cond-mat.str-el↗

arXiv2024

Borophane as substrate for adsorption of He-4: A journey across dimensionality

In search of substrates for adsorption of He atoms allowing for novel quantum phases in restricted geometry we study the case of borophane. We focus on two allotropes of borophane, alpha-4H and Rect-2H. With a suitable Density Functional Theory we characterize the adsorption potential of a He atom on such crystalline substrates finding its corrugation, the preferential adsorption sites and the energy barrier between sites. Rect-2H borophane is particularly interesting due to thepresence of ridges in the adsorption potential with modest energy barriers in one direction of the basal plane and much higher barrier in the orthogonal direction, thus forming channels for motion of the adsorbed atoms. We study the adsorption of He-4 on Rect-2H borophane using Path Integral Monte Carlo simulations. In the first adsorbed layer the He-4 atoms are rather delocalized along a channel with no exchanges between channels. This strong anisotropy is present also in the first few additional adsorption layers of He-4 with presence of ordered and of disordered regions. In the second and the fifth layers at low temperature we find superfluidity on the length scale of the simulated systems. In the second layer the superfluidity is one-dimensional along the grooves. In the fifth layer the state is a strongly anisotropic two-dimensional superfluid at low coverage, with a crossover to an isotropic one at layer completion. Starting from the sixth layer the adsorbed He-4 film evolves toward a three-dimensional superfluid. Our main prediction is that Rect-2H borophane as a substrate will allow to probe 1D superfluidity in the second absorption layer, as well as the evolution from a 2D anisotropic superfluid to an isotropic one in the fifth layer, and eventually the onset of 3D superfluidity for higher coverages.

cond-mat.mes-hall↗

arXiv2024

Liquid-liquid transition in a Bose fluid near collapse

Discovering novel emergent behavior in quantum many-body systems is a main objective of contemporary research. In this paper, we explore the effects on phases and phase transitions of the proximity to a Ruelle-Fisher instability, marking the transition to a collapsed state. To accomplish this, we study by quantum Monte Carlo simulations a two-dimensional system of soft-core bosons interacting through an isotropic finite-ranged attraction, with a parameter $η$ describing its strength. If $η$ exceeds a characteristic value $η_c$, the thermodynamic limit is lost, as the system becomes unstable against collapse. We investigate the phase diagram of the model for $η\lesssimη_c$, finding -- in addition to a liquid-vapor transition -- a first-order transition between two liquid phases. Upon cooling, the high-density liquid turns superfluid, possibly above the vapor-liquid-liquid triple temperature. As $η$ approaches $η_c$, the stability region of the high-density liquid is shifted to increasingly higher densities, a behavior at variance with distinguishable quantum or classical particles. Finally, for $η$ larger than $η_c$ our simulations yield evidence of collapse of the low-temperature fluid for any density; the collapsed system forms a circular cluster whose radius is insensitive to the number of particles.

cond-mat.stat-mech↗

arXiv2024

Accurate quantum Monte Carlo forces for machine-learned force fields: Ethanol as a benchmark

Quantum Monte Carlo (QMC) is a powerful method to calculate accurate energies and forces for molecular systems. In this work, we demonstrate how we can obtain accurate QMC forces for the fluxional ethanol molecule at room temperature by using either multi-determinant Jastrow-Slater wave functions in variational Monte Carlo or just a single determinant in diffusion Monte Carlo. The excellent performance of our protocols is assessed against high-level coupled cluster calculations on a diverse set of representative configurations of the system. Finally, we train machine-learning force fields on the QMC forces and compare them to models trained on coupled cluster reference data, showing that a force field based on the diffusion Monte Carlo forces with a single determinant can faithfully reproduce coupled cluster power spectra in molecular dynamics simulations.

physics.chem-ph↗

arXiv2023

Wave function Ansatz (but Periodic) Networks and the Homogeneous Electron Gas

We design a neural network Ansatz for variationally finding the ground-state wave function of the Homogeneous Electron Gas, a fundamental model in the physics of extended systems of interacting fermions. We study the spin-polarised and paramagnetic phases with 7, 14 and 19 electrons over a broad range of densities from $r_s=1$ to $r_s=100$, obtaining similar or higher accuracy compared to a state-of-the-art iterative backflow baseline even in the challenging regime of very strong correlation. Our work extends previous applications of neural network Ansätze to molecular systems with methods for handling periodic boundary conditions, and makes two notable changes to improve performance: splitting the pairwise streams by spin alignment and generating backflow coordinates for the orbitals from the network. We illustrate the advantage of our high quality wave functions in computing the reduced single particle density matrix. This contribution establishes neural network models as flexible and high precision Ansätze for periodic electronic systems, an important step towards applications to crystalline solids.

physics.chem-ph↗

arXiv2022

Superfluid transition of the second layer of He-4 on graphite: does substrate corrugation matter?

The second layer of He-4 adsorbed on a graphite substrate is studied by Quantum Monte Carlo simulations. We make use of a microscopic model of the substrate fully accounting for its corrugation, and compare the results to those obtained with a smooth substrate. The only effect of corrugation is a ~20% reduction of the value of the superfluid fraction of the top layer, in the limit of zero temperature. No evidence of any commensurate (7/12) crystalline and/or "supersolid" phase is found; the superfluid transition temperature is estimated to be ~ 0.75 K. We discuss the implication of these findings on the interpretation of recent experiments.

cond-mat.stat-mech↗

arXiv2022

Double excitation energies from quantum Monte Carlo using state-specific energy optimization

We show that recently developed quantum Monte Carlo methods, which provide accurate vertical transition energies for single excitations, also successfully treat double excitations. We study the double excitations in medium-sized molecules, some of which are challenging for high level coupled-cluster calculations to model accurately. Our fixed-node diffusion Monte Carlo excitation energies are in very good agreement with reliable benchmarks, when available, and provide accurate predictions for excitation energies of difficult systems where reference values are lacking.

physics.comp-ph↗

arXiv2022

Quadriexcitons and excitonic condensate in a symmetric electron-hole bilayer with valley degeneracy

Using quantum Monte Carlo simulations we have mapped out the zero temperature phase diagram of a symmetric electron-hole bilayer with twofold valley degeneracy, as function of the interlayer distance $d$ and in-layer density $n$. We find that the effect of the valley degeneracy is to shrink the region of stability of the excitonic condensate, in favor of quadriexcitons at small $d$ and of the four-component plasma at large $d$, with minor effects on the value of the excitonic condensate fraction. The enclosure of the condensate in a density window possibly explains why anomalous tunnelling conductivity, interpreted as signature of condensation, is observed only between two finite values of carrier density in graphene bilayers. Our phase diagram may provide directions to select device parameters for future experiments.

cond-mat.str-el↗

arXiv2021

Reference excitation energies of increasingly large molecules: a QMC study of cyanine dyes

We revisit here the lowest vertical excitations of cyanine dyes using quantum Monte Carlo and leverage on recent developments to systematically improve on previous results. In particular, we employ a protocol for the construction of compact and accurate multi-determinant Jastrow-Slater wave functions for multiple states, which we have recently validated on the excited-state properties of several small prototypical molecules. Here, we obtain quantum Monte Carlo excitation energies in excellent agreement with high-level coupled cluster for all the cyanines where the coupled cluster method is applicable. Furthermore, we push our protocol to longer chains, demonstrating that quantum Monte Carlo is a viable methodology to establish reference data at system sizes which are hard to reach with other high-end approaches of similar accuracy. Finally, we determine which ingredients are key to an accurate treatment of these challenging systems and rationalize why a description of the excitation based on only active $π$ orbitals lacks the desired accuracy for the shorter chains.

physics.chem-ph↗

arXiv2021

Localization versus inhomogeneous superfluidity: Submonolayer He-4 on fluorographene, hexagonal boron nitride, and graphene

We study a sub monolayer He-4 adsorbed on fluorographene (GF) and on hexagonal boron nitride (hBN) at low coverage. The adsorption potentials have been computed ab-initio with a suitable density functional theory including dispersion forces. The properties of the adsorbed He-4 atoms have been computed at finite temperature with path integral Monte Carlo and at T=0 K with variational path integral. From both methods we find that the lowest energy state of He-4 on GF is a superfluid. Due to the very large corrugation of the adsorption potential this superfluid has a very strong spatial anisotropy, the ratio between the largest and smallest areal density being about 6, the superfluid fraction at the lowest T is about 55%, and the temperature of the transition to the normal state is in the range 0.5-1 K. Thus, GF offers a platform for studying the properties of a strongly interacting highly anisotropic bosonic superfluid. At a larger coverage He-4 has a transition to an ordered commensurate state with occupation of 1/6 of the adsorption sites. This phase is stable up to a transition temperature located between 0.5 and 1~K. The system has a triangular order similar to that of He-4 on graphite. The lowest energy state of He-4 on hBN is an ordered commensurate state with occupation of 1/3 of the adsorption sites and triangular symmetry. A disordered state is present at lower coverage as a metastable state. In the presence of an electric field the corrugation of the adsorption potential is slightly increased but up to a magnitude of 1 V/Ang. the effect is small and does not change the stability of the phases of He-4 on GF and hBN. We have verified that also in the case of graphene such electric field does not modify the stability of the commensurate sqrt{3}*sqrt{3}R30 phase.

cond-mat.other↗

arXiv2021

Energy derivatives in real-space diffusion Monte Carlo

We present unbiased, finite--variance estimators of energy derivatives for real--space diffusion Monte Carlo calculations within the fixed--node approximation. The derivative $d_λE$ is fully consistent with the dependence $E(λ)$ of the energy computed with the same time step. We address the issue of the divergent variance of derivatives related to variations of the nodes of the wave function, both by using a regularization for wave function parameter gradients recently proposed in variational Monte Carlo, and by introducing a regularization based on a coordinate transformation. The essence of the divergent variance problem is distilled into a particle-in-a-box toy model, where we demonstrate the algorithm.

cond-mat.mtrl-sci↗

arXiv2021

Tailoring CIPSI expansions for QMC calculations of electronic excitations: the case study of thiophene

The perturbatively selected configuration interaction scheme (CIPSI) is particularly effective in constructing determinantal expansions for quantum Monte Carlo (QMC) simulations with Jastrow-Slater wave functions: fast and smooth convergence of ground-state properties, as well as balanced descriptions of ground- and excited-states of different symmetries have been reported. In particular, accurate excitation energies have been obtained by the pivotal requirement of using CIPSI expansions with similar second-order perturbation corrections for each state, that is, similar estimated errors with respect to the full configuration interaction limit. Here we elaborate on the CIPSI selection criterion for excited states of the same symmetry as the ground state, generating expansions from a common orbital set. Using these expansions in QMC as determinantal components of Jastrow-Slater wave functions, we compute the lowest, bright excited state of thiophene, which is challenging due to its significant multireference character. The resulting vertical excitation energies are within 0.05~eV of the best theoretical estimates, already with expansions of only a few thousand determinants. Furthermore, we relax the ground- and excited-state structures following the corresponding root in variational Monte Carlo and obtain bond lengths which are accurate to better than 0.01~Å. Therefore, while the full treatment at the CIPSI level of this system would be quite demanding, in QMC we can compute high-quality excitation energies and excited-state structural parameters building on affordable CIPSI expansions with relatively few, well chosen determinants.

physics.class-ph↗

arXiv2020

Specific heat of thin $^4$He films on graphite

The specific heat of a two-layer He-4 film adsorbed on a graphite substrate is estimated as a function of temperature by Quantum Monte Carlo simulations. The results are consistent with recent experimental observations, in that they broadly reproduce their most important features. However, neither the "supersolid" nor the "superfluid hexatic" phases, of which experimental data are claimed to be evidence, are observed. It is contended that heat capacity measurements alone may not be a good predictor of structural and superfluid transitions in this system, as their interpretation is often ambiguous.

cond-mat.stat-mech↗

arXiv2020

Itinerant-electron magnetism: the importance of many-body correlations

Do electrons become ferromagnetic just because of their repulisve Coulomb interaction? Our calculations on the three-dimensional electron gas imply that itinerant ferromagnetim of delocalized electrons without lattice and band structure, the most basic model considered by Stoner, is suppressed due to many-body correlations as speculated already by Wigner, and a possible ferromagnetic transition lowering the density is precluded by the formation of the Wigner crystal.

cond-mat.str-el↗

arXiv2020

Variational principles in quantum Monte Carlo: the troubled story of variance minimization

We investigate the use of different variational principles in quantum Monte Carlo, namely energy and variance minimization, prompted by the interest in the robust and accurate estimate of electronic excited states. For two prototypical, challenging molecules, we readily reach the accuracy of the best available reference excitation energies using energy minimization in a state-specific or state-average fashion for states of different or equal symmetry, respectively. On the other hand, in variance minimization, where the use of suitable functionals is expected to target specific states regardless of the symmetry, we encounter severe problems for a variety of wave functions: as the variance converges, the energy drifts away from that of the selected state. This unexpected behavior is sometimes observed even when the target is the ground state, and generally prevents the robust estimate of total and excitation energies. We analyze this problem using a very simple wave function and infer that the optimization finds little or no barrier to escape from a local minimum or local plateau, eventually converging to the unique lowest-variance state instead of the target state. While the loss of the state of interest can be delayed and possibly avoided by reducing the statistical error of the gradient, for the full optimization of realistic wave functions, variance minimization with current functionals appears to be an impractical route.

physics.chem-ph↗

arXiv2019

Orbital-dependent backflow wave functions for real-space quantum Monte Carlo

We present and motivate an efficient way to include orbital dependent many--body correlations in trial wave function of real--space Quantum Monte Carlo methods for use in electronic structure calculations. We apply our new orbital--dependent backflow wave function to calculate ground state energies of the first row atoms using variational and diffusion Monte Carlo methods. The systematic overall gain of correlation energy with respect to single determinant Jastrow-Slater wave functions is competitive with the best single determinant trial wave functions currently available. The computational cost per Monte Carlo step is comparable to that of simple backflow calculations.

physics.comp-ph↗