arXiv subjects

Michele Casula

Publications and source records attributed to Michele Casula.

At least 19 recordsLinked to original sources

arXiv2026

Quadrupolar phase transition in superconducting lanthanum hydride

Lanthanum hydride (LaH$_{10}$) has been widely studied for its high superconducting critical temperature of 250 K at about 170 GPa pressure. Although the structural ${R\bar{3}m}$-to-${Fm\bar{3}m}$ transition under pressure connected to the emergence of the superconducting phase in this material is broadly understood, the detailed characterization of its nature and its order parameter are still missing. By applying the cluster multipole moment analysis to the hydrogen sublattice, we reveal that this transition is triggered by a quadrupolar $T_{2g}$ order parameter, and we provide evidence for its weak first-order nature. By performing path integral molecular dynamics coupled to a message-passing atomic cluster expansion (MACE) neural network potential, trained on Perdew-Burke-Ernzerhof (PBE) density functional theory configurations, we show that the collapse of the order parameter at the transition is simultaneously associated with the discontinuous softening of the optical $T_{2g}$ phonons. Their symmetry lets them carry a non-negligible electron-phonon coupling in LaH$_{10}$, while the weak first-order nature of the transition makes them soft. The presence of structural instabilities with low-frequency quadrupolar distortions can be a key ingredient to enhance superconductivity in superhydrides and provides guidance for the discovery of new high-$T_c$ superconductors in hydrogen-rich compounds.

cond-mat.supr-con↗

arXiv2026

Negative Thermal Expansion in Cubic Ice: A Collective Quantum Effect of the hydrogen-bond network

We report neutron powder diffraction measurements and path-integral molecular dynamics simulations of stacking-disorder-free cubic ice I$_c$, produced by topotactic degassing of C2 hydrogen hydrate. Across the cryogenic stability range, ice I$_c$ exhibits a density maximum near 70 K, closely matching that of hexagonal ice I$_h$ despite their different long-range stacking sequences. Negative thermal expansion in ice I is therefore not specific to hexagonal stacking, but arises from the shared open tetrahedral hydrogen-bond network. Simulations with the MB-pol potential quantitatively reproduce the experimental anomaly only when nuclear quantum effects are included. The density maximum coincides, within the temperature resolution, with maximal anisotropy of the proton quantum distribution. Neutron-derived displacement parameters independently reveal a strongly enhanced transverse proton displacement, while phonon calculations identify low-frequency transverse modes with the most negative Grüneisen parameters. Together, these results establish the negative thermal expansion of ice I as a collective quantum effect governed by nuclear statistics and the dynamics of the hydrogen-bond network.

cond-mat.mtrl-sci↗

arXiv2026

jQMC: A JAX-based ab initio quantum Monte Carlo package designed for GPU-accelerated computing

We present jQMC, a Python-based computational package for {\it ab initio} Quantum Monte Carlo (QMC) simulations, designed for modern GPU-accelerated computing environments. jQMC implements two well-established QMC algorithms: Variational Monte Carlo (VMC) and the lattice-regularized variant of Diffusion Monte Carlo (LRDMC). The employed wave function is a Jastrow factor combined with the antisymmetrized geminal power with spin-singlet and spin-triplet pairings, which contains the single Slater determinant as its special lowest-rank case. The wave function can be initialized from external Hartree-Fock/Density Functional Theory calculations through the TREX-IO library (a common wave-function format across electronic-structure packages) and optimized by stochastic reconfiguration and linear-method energy minimization. One of the prominent features of jQMC is its use of JAX, which enables automatic differentiation for wave function optimization and atomic force calculations, and allows the main QMC algorithms to be Just-In-Time (JIT) compiled and portable across CPU and GPU. jQMC is vectorized over walkers at the top level of the QMC algorithms, providing efficient intra-GPU~(CPU) vectorization. The multi-GPU~(CPU) parallelization is also supported through MPI and JAX sharding. To assess the practical performance of this implementation, we benchmarked jQMC performance on NVIDIA GPUs (A100 and H100) and analyzed CUDA kernels. For the test cases analyzed here, with system sizes up to 160 electrons, the current version of jQMC is faster than TurboRVB, a Fortran90 code implementing the same algorithms and wave functions, once jQMC is run on GPUs. In terms of wall-time, the gain can reach an order of magnitude for VMC, while it is more moderate for LRDMC.

physics.chem-ph↗

arXiv2026

Displacive quantum critical point in superconducting hydrides: The case of H$_3$S

H$_3$S sulfur hydride has been widely investigated for its high superconducting critical temperature $T_c$ of 203 K at about $p_c = 155$ GPa. Despite being the precursor of superconducting hydrides, a detailed picture of its structural phase diagram in an extended temperature and pressure range is still missing. To determine it with inclusion of both thermal and quantum effects, we carry out path integral molecular dynamics combined to a MACE neural network potential trained on BLYP density functional theory configurations. The resulting H$_3$S phase diagram is characterized by the displacive transition between the centrosymmetric Im$\bar{3}$m and polar R3m phases, which originates from a quantum critical point (QCP) located at $p_\mathrm{QCP} \approx 134$ GPa. We show that the experimental $T_c$ peak falls into a centrosymmetric region of large nuclear quantum fluctuations above the displacive QCP, as measured by local phonon Green's functions resolved in imaginary time, where fluctuating moments are at play. We study the critical behavior of the system in the proximity of the QCP by a finite-size scaling analysis, showing that it belongs to the 4D Ising universality class. We finally discuss its implications for the superconducting state.

cond-mat.supr-con↗

arXiv2026

Spin-polaron fingerprints in the optical conductivity of iridates

As a consequence of their spin-orbit entangled ground state, many $5d^{5}$ iridate materials display a peculiar double peak structure in optical transport quantities, such as absorption and conductivity. Their common interpretation is based on the presence of Hubbard subbands in the half-filled $j_{\mathrm{eff}}=1/2$ manifold. Herein, we challenge this picture, proposing a scenario based on the presence of spin-polaron (SP) quasiparticles, and assigning a dominant SP character to the first peak. We illustrate it by taking the materials Ba$_2$IrO$_4$ and Sr$_2$IrO$_4$ as paradigmatic examples, which we investigate within the dynamical mean-field theory and the self-consistent Born approximation. Both theories reproduce nontrivial features revealed by angle-resolved photoemission spectroscopy and optical transport measurements, supporting our interpretation. In the case of Sr$_2$IrO$_4$, we show how the SP scenario survives in the low-doped regime. Similar optical transport fingerprints are expected to be found in the wider class of $5d^5$ iridates and more generally in strongly correlated antiferromagnetic regimes, such as those found in cuprates.

cond-mat.str-el↗

arXiv2026

Antiferromagnetic stripe phase and large-gap insulating ground state of the correlated $\sqrt{3}\times\sqrt{3}$~R30$^{\circ}$-Sn/Si(111) single atomic layer

The one-third monolayer Sn layer on Si(111) has long been considered a benchmark system for exploring two-dimensional Mott physics, owing to its narrow bandwidth and sizable on-site Coulomb repulsion. Previous experiments suggested the emergence of a low-temperature Mott insulating phase with an energy gap of only a few tens of meV, while theory predicted a possible antiferromagnetic ordering that remained experimentally elusive. Here, by combining low-temperature scanning tunneling microscopy/spectroscopy with first-principles calculations, we reveal that the $\sqrt{3}\times\sqrt{3}$~R30$^{\circ}$-Sn/Si(111) surface undergoes a transition below 30K into a robust insulating state characterized by a remarkably large gap of about 440 $\pm$ 120 meV at 4K, five to ten times larger than previously reported. Quasiparticle interference imaging uncovers a well-defined $2\sqrt{3}\times\sqrt{3}$~R30$^{\circ}$-Sn/Si(111) superstructure, providing direct evidence for a two-dimensional stripe-like antiferromagnetic order. Ab initio calculations reveal that the silicon substrate stabilizes this phase through strong nonlocal tin-tin interactions, highlighting the decisive role of substrate-driven correlations in the $\sqrt{3}\times\sqrt{3}$~R30$^{\circ}$-Sn/Si(111) system.

cond-mat.str-el↗

arXiv2025

Hydrogen liquid-liquid transition from first principles and machine learning

The molecular-to-atomic liquid-liquid transition (LLT) in high-pressure hydrogen is a fundamental topic touching domains from planetary science to materials modeling. Yet, the nature of the LLT is still under debate. To resolve it, numerical simulations must cover length and time scales spanning several orders of magnitude. We overcome these size and time limitations by constructing a fast and accurate machine-learning interatomic potential (MLIP) built on the MACE neural network architecture. The MLIP is trained on Perdew-Burke-Ernzerhof (PBE) density functional calculations and uses a modified loss function correcting for an energy bias in the molecular phase. Classical and path-integral molecular dynamics driven by this MLIP show that the LLT is always supercritical above the melting temperature. The position of the corresponding Widom line agrees with previous ab initio PBE calculations, which in contrast predicted a first-order LLT. According to our calculations, the crossover line becomes a first-order transition only inside the molecular crystal region. These results call for a reconsideration of the LLT picture previously drawn.

cond-mat.dis-nn↗

arXiv2025

Self-consistency error correction for accurate machine learning potentials from variational Monte Carlo

Variational Monte Carlo (VMC) can be used to train accurate machine learning interatomic potentials (MLIPs), enabling molecular dynamics (MD) simulations of complex materials on time scales and for system sizes previously unattainable. VMC training sets are often based on partially optimized wave functions (WFs) to circumvent expensive energy optimizations of the whole set of WF parameters. However, frozen variational parameters lead to VMC forces and pressures not consistent with the underlying potential energy surface, a bias called the self-consistency error (SCE). Here, we demonstrate how the SCE can spoil the accuracy of MLIPs trained on these data, taking high-pressure hydrogen as test case. We then apply a recently introduced SCE correction [ Phys. Rev. B 109, 205151 (2024)] to generate unbiased VMC training sets based on a Jastrow-correlated single determinant WF with frozen Kohn-Sham orbitals. The MLIPs generated within this framework are significantly improved and can approach in quality those trained on datasets built with fully optimized WFs. Our conclusions are further supported by MD simulations, which show how MLIPs trained on SCE-corrected datasets systematically yield more reliable physical observables. Our framework opens the possibility of constructing extended high-quality training sets with VMC.

cond-mat.str-el↗

arXiv2025

Dual quantum locking: Dynamic coupling of hydrogen and water sublattices in hydrogen filled ice

Hydrogen hydrates (HH) are a unique class of materials composed of hydrogen molecules confined within crystalline water frameworks. Among their multiple phases, the filled ice structures, particularly the cubic C2 phase, exhibit exceptionally strong host-guest interactions due to ultra-short H2-H2O distances and a 1:1 stoichiometry leading to two interpenetrated identical diamond-like sublattices, one comprised of water molecules, the other of hydrogen molecules. At high pressures, nuclear quantum effects involving both hydrogen molecules and the water lattice become dominant, giving rise to a dual-lattice quantum system. In this work, we explore the sequence of pressure- and temperature-driven phase transitions in HH, focusing on the interplay between molecular rotation, orientational ordering, lattice symmetry breaking and hydrogen bond symmetrization. Using a combination of computational modeling based on classical and path-integral molecular dynamics, quantum embedding, and high pressure experiments, including Raman spectroscopy and synchrotron X-ray diffraction at low temperatures and high pressures, we identify signatures of quantum-induced ordering and structural transformations in the C2 phase. Our findings reveal that orientational ordering in HH occurs at much lower pressures than in solid hydrogen, by inducing structural changes in the water network and enhancing the coupling of water and hydrogen dynamics. This work provides new insights into the quantum behavior of hydrogen under extreme mechanochemical confinement and establishes hydrogen-filled ices as a promising platform for the design of hydrogen-rich quantum materials.

cond-mat.mtrl-sci↗

arXiv2025

Reproducibility of fixed-node diffusion Monte Carlo across diverse community codes: The case of water-methane dimer

Fixed-node diffusion quantum Monte Carlo (FN-DMC) is a widely-trusted many-body method for solving the Schrödinger equation, known for its reliable predictions of material and molecular properties. Furthermore, its excellent scalability with system complexity and near-perfect utilization of computational power makes FN-DMC ideally positioned to leverage new advances in computing to address increasingly complex scientific problems. Even though the method is widely used as a computational gold standard, reproducibility across the numerous FN-DMC code implementations has yet to be demonstrated. This difficulty stems from the diverse array of DMC algorithms and trial wave functions, compounded by the method's inherent stochastic nature. This study represents a community-wide effort to assess the reproducibility of the method, affirming that: Yes, FN-DMC is reproducible (when handled with care). Using the water-methane dimer as the canonical test case, we compare results from eleven different FN-DMC codes and show that the approximations to treat the non-locality of pseudopotentials are the primary source of the discrepancies between them. In particular, we demonstrate that, for the same choice of determinantal component in the trial wave function, reliable and reproducible predictions can be achieved by employing the T-move (TM), the determinant locality approximation (DLA), or the determinant T-move (DTM) schemes, while the older locality approximation (LA) leads to considerable variability in results. These findings demonstrate that, with appropriate choices of algorithmic details, fixed-node DMC is reproducible across diverse community codes-highlighting the maturity and robustness of the method as a tool for open and reliable computational science.

physics.comp-ph↗

arXiv2025

Load-Balanced Diffusion Monte Carlo Method with Lattice Regularization

Ab initio quantum Monte Carlo (QMC) is a stochastic approach for solving the many-body Schrödinger equation without resorting to one-body approximations. QMC algorithms are readily parallelizable via ensembles of $N_w$ walkers, making them well suited to large-scale high-performance computing. Among the QMC techniques, Diffusion Monte Carlo (DMC) is widely regarded as the most reliable, since it provides the projection onto the ground state of a given Hamiltonian under the fixed-node approximation. One practical realization of DMC is the Lattice Regularized Diffusion Monte Carlo (LRDMC) method, which discretizes the Hamiltonian within the Green's Function Monte Carlo framework. DMC methods - including LRDMC - employ the so-called branching technique to stabilize walker weights and populations. At the branching step, walkers must be synchronized globally; any imbalance in per-walker workload can leave CPU or GPU cores idle, thereby degrading overall hardware utilization. The conventional LRDMC algorithm intrinsically suffers from such load imbalance, which grows as $\log(N_w)$, rendering it less efficient on modern parallel architectures. In this work, we present an LRDMC algorithm that inherently addresses the load imbalance issue and achieves significantly improved weak-scaling parallel efficiency. Using the binding energy calculation of a water-methane complex as a test case, we demonstrated that the conventional and load-balanced LRDMC algorithms yield consistent results. Furthermore, by utilizing the Leonardo supercomputer equipped with NVIDIA A100 GPUs, we demonstrated that the load-balanced LRDMC algorithm can maintain extremely high parallel efficiency ($\sim$98\%) up to 512 GPUs (corresponding to $N_{\rm w}= 51200$), together with a speedup of $\times~1.24$ if directly compared with the conventional LRDMC algorithm with the same number of walkers.

physics.chem-ph↗

arXiv2024

Assessing many-body methods on the potential energy surface of the (H$_2$)$_2$ hydrogen dimer

The anisotropic potential energy surface of the (H$_2$)$_2$ dimer represents a challenging problem for many-body methods. Here, we determine the potential energy curves of five different dimer configurations (T, Z, X, H, L) using the lattice regularized diffusion Monte Carlo (LRDMC) method and a number of approximate functionals within density functional theory (DFT), including advanced orbital-dependent functionals based on the random phase approximation (RPA). We assess their performance in describing the potential wells, bond distances and relative energies. The repulsive potential wall is studied by looking at the relative stability of the different dimer configurations as a function of an applied force acting along the intermolecular axis. It is shown that most functionals within DFT break down at finite compression, even those that give an accurate description around the potential well minima. Only by including exchange within RPA a qualitatively correct description along the entire potential energy curve is obtained. Finally, we discuss these results in the context of solid molecular hydrogen at finite pressures.

physics.chem-ph↗

arXiv2024

Efficient calculation of unbiased atomic forces in ab initio Variational Monte Carlo

Ab initio quantum Monte Carlo (QMC) is a state-of-the-art numerical approach for evaluating accurate expectation values of many-body wavefunctions. However, one of the major drawbacks that still hinders widespread QMC applications is the lack of an affordable scheme to compute unbiased atomic forces. In this study, we propose a very efficient method to obtain unbiased atomic forces and pressures in the Variational Monte Carlo (VMC) framework with the Jastrow-correlated Slater determinant ansatz, exploiting the gauge-invariant and locality properties of its geminal representation. We demonstrate the effectiveness of our method for H$_2$ and Cl$_2$ molecules and for the cubic boron nitride crystal. Our framework has a better algorithmic scaling with the system size than the traditional finite-difference method, and, in practical applications, is as efficient as single-point VMC calculations. Thus, it paves the way to study dynamical properties of materials, such as phonons, and is beneficial for pursuing more reliable machine-learning interatomic potentials based on unbiased VMC forces.

cond-mat.mtrl-sci↗

arXiv2024

Principal deuterium Hugoniot via Quantum Monte Carlo and $Δ$-learning

We present a study of the principal deuterium Hugoniot for pressures up to $150$ GPa, using Machine Learning potentials (MLPs) trained with Quantum Monte Carlo (QMC) energies, forces and pressures. In particular, we adopted a recently proposed workflow based on the combination of Gaussian kernel regression and $Δ$-learning. By fully taking advantage of this method, we explicitly considered finite-temperature electrons in the dynamics, whose effects are highly relevant for temperatures above $10$ kK. The Hugoniot curve obtained by our MLPs shows a good agreement with the most recent experiments, particularly in the region below 60 GPa. At larger pressures, our Hugoniot curve is slightly more compressible than the one yielded by experiments, whose uncertainties generally increase, however, with pressure. Our work demonstrates that QMC can be successfully combined with $Δ$-learning to deploy reliable MLPs for complex extended systems across different thermodynamic conditions, by keeping the QMC precision at the computational cost of a mean-field calculation.

cond-mat.str-el↗

arXiv2024

Quantum effects in the H-bond symmetrization and in the thermodynamic properties of high pressure ice

We investigate the structural and thermodynamic properties of high-pressure ice by incorporating quantum anharmonicity at a non-perturbative level. Quantum fluctuations reduce the critical pressure of the phase transition between phase VIII (with asymmetric H-bonds) and phase X (with symmetric H-bonds) by 65 GPa from its classical value of 116 GPa at 0K. Moreover, quantum effects make it temperature-independent over a wide temperature range (0K-300K), in agreement with experimental estimates obtained through vibrational spectroscopy and in striking contrast to the strong temperature dependence found in the classical approximation. The equation of state shows fingerprints of the transition in accordance with experimental evidence. Additionally, we demonstrate that, within our approach, proton disorder in phase VII has a negligible impact on the occurrence of phase X. Finally, we reproduce with high accuracy the 10 GPa isotope shift due to the hydrogen-to-deuterium substitution.

cond-mat.other↗

arXiv2023

Rényi entropy of quantum anharmonic chain at non-zero temperature

The interplay of quantum and classical fluctuations in the vicinity of a quantum critical point (QCP) gives rise to various regimes or phases with distinct quantum character. In this work, we show that the Rényi entropy is a precious tool to characterize the phase diagram of critical systems not only around the QCP but also away from it, thanks to its capability to detect the emergence of local order at finite temperature. For an efficient evaluation of the Rényi entropy, we introduce a new algorithm based on a path integral Langevin dynamics combined with a previously proposed thermodynamic integration method built on regularized paths. We apply this framework to study the critical behavior of a linear chain of anharmonic oscillators, a particular realization of the $ϕ^4$ model. We fully resolved its phase diagram, as a function of both temperature and interaction strength. At finite temperature, we find a sequence of three regimes - para, disordered and quasi long-range ordered -, met as the interaction is increased. The Rényi entropy divergence coincides with the crossover between the para and disordered regime, which shows no temperature dependence. The occurrence of quasi long-range order, on the other hand, is temperature dependent. The two crossover lines merge in proximity of the QCP, at zero temperature, where the Rényi entropy is sharply peaked. Via its subsystem-size scaling, we confirm that the transition belongs to the two-dimensional Ising universality class. This phenomenology is expected to happen in all $ϕ^4$-like systems, as well as in the elusive water ice transition across phases VII, VIII and X.

cond-mat.stat-mech↗

arXiv2023

Quantum symmetrization transition in superconducting sulfur hydride from quantum Monte Carlo and path integral molecular dynamics

We study the structural phase transition, originally associated with the highest superconducting critical temperature $T_c$ measured in high-pressure sulfur hydride. A quantitative description of its pressure dependence has been elusive for any \emph{ab initio} theory attempted so far, raising questions on the actual mechanism leading to the maximum of $T_c$. Here, we estimate the critical pressure of the hydrogen bond symmetrization in the Im$\bar{3}$m structure, by combining density functional theory and quantum Monte Carlo simulations for electrons with path integral molecular dynamics for quantum nuclei. We find that the $T_c$ maximum corresponds to pressures where local dipole moments dynamically form on the hydrogen sites, as precursors of the ferroelectric Im$\bar{3}$m-R3m transition, happening at lower pressures. For comparison, we also apply the self-consistent harmonic approximation, whose ferroelectric critical pressure lies in between the ferroelectric transition estimated by path integral molecular dynamics and the local dipole formation. Nuclear quantum effects play a major role in a significant reduction ($\approx$ 50 GPa) of the classical ferroelectric transition pressure at 200K and in a large isotope shift ($\approx$ 25 GPa) upon hydrogen-to-deuterium substitution of the local dipole formation pressure, in agreement with the corresponding change in the $T_c$ maximum location.

cond-mat.str-el↗

arXiv2023

The rich phase diagram of the prototypical iridate Ba$_2$IrO$_4$: Effective low-energy models and metal-insulator transition

In the quest of new exotic phases of matter due to the interplay of various interactions, iridates hosting a spin-orbit entangled $j_{\mathrm{eff}}=1/2$ ground state have been in the spotlight in recent years. Also in view of parallels with the low-energy physics of high-temperature superconducting cuprates, the validity of a single- or few-band picture in terms of the $j_{\mathrm{eff}}$ states is key. However, in particular for its structurally simple member Ba$_2$IrO$_4$, such a systematic construction and subsequent analysis of minimal low-energy models are still missing. Here we show by means of a combination of different ab initio techniques with dynamical mean-field theory that a three-band model in terms of Ir-$j_{\mathrm{eff}}$ states fully retains the low-energy physics of the system as compared to a full Ir-$5d$ model. Providing a detailed study of the three-band model in terms of spin-orbit coupling, Hund's coupling and Coulomb interactions, we map out a rich phase diagram and identify a region of effective one-band metal-insulator transition relevant to Ba$_2$IrO$_4$. Compared to available angle-resolved photoemission spectra, we find good agreement of salient aspects of the calculated spectral function and identify features which require the inclusion of non-local fluctuations. In a broader context, we envisage the three- and five-band models developed in this study to be relevant for the study of doped Ba$_2$IrO$_4$ and to clarify further the similarities and differences with cuprates.

cond-mat.str-el↗