Spin-Orbit Quantum Monte Carlo for heavy element Equations of state
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Clay III, Raymond C. [Sandia National Laboratories↗
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Results for “Quantum Monte Carlo”
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Theoretical Studies of Liquid He-4 Near the Superfluid Transition
We performed theoretical studies of liquid helium by applying state of the art simulation and finite-size scaling techniques. We calculated universal scaling functions for the specific heat and superfluid density for various confining geometries relevant for experiments such as the confined helium experiment and other ground based studies. We also studied microscopically how the substrate imposes a boundary condition on the superfluid order parameter as the superfluid film grows layer by layer. Using path-integral Monte Carlo, a quantum Monte Carlo simulation method, we investigated the rich phase diagram of helium monolayer, bilayer and multilayer on a substrate such as graphite. We find excellent agreement with the experimental results using no free parameters. Finally, we carried out preliminary calculations of transport coefficients such as the thermal conductivity for bulk or confined helium systems and of their scaling properties. All our studies provide theoretical support for various experimental studies in microgravity.
Manousakis, Efstratios↗
Quantum Zeno Monte Carlo for computing observables
The recent development of logical quantum processors marks a pivotal transition from the noisy intermediate-scale quantum (NISQ) era to the fault-tolerant quantum computing (FTQC) era. These devices have the potential to address classically challenging problems with polynomial computational time using quantum properties. However, they remain susceptible to noise, necessitating noise resilient algorithms. We introduce Quantum Zeno Monte Carlo (QZMC), a classical-quantum hybrid algorithm that demonstrates resilience to device noise and Trotter errors while showing polynomial computational cost for a gapped system. QZMC computes static and dynamic properties without requiring initial state overlap or variational parameters, offering reduced quantum circuit depth.
Han, Mancheon [Korea Institute for Advanced Study ↗
Multireference diffusion Monte Carlo reaches 2D materials
Abstract Quantum confinement in 2D materials strongly enhances electronic correlation effects. Therefore, predicting the properties of these unique materials, with both a high level of accuracy and computational efficiency, without relying on adjustable parameters or functionals, remains an outstanding theoretical challenge. The majority of theoretical studies are based on the approximations of density functional theory (DFT). The reliability of DFT predictions are heavily dependent on the choice of an approximated exchange-correlation functional. Here, we estimate the magnitude of impact of correlation on the total energy for the quintessential 2D material, graphene, by performing and comparing state-of-the-art selected CI and quantum Monte Carlo extrapolated calculations for a single unit cell at the$$\Gamma$$point. We demonstrate that Self-Healing Diffusion Monte Carlo (SHDMC) obtains a very compact, but high-quality wavefunction for this system that lacks the strong basis set dependence displayed by state of the art quantum chemistry methods. The SHDMC wavefunction is of higher quality compared to that obtained from sCI, in the same orbital basis, while being$$\sim$$ 1000 times smaller in terms of determinant count compared to sCI. We also demonstrate that extrapolating SHDMC results to the infinite determinant limit compares extremely well with complete basis set extrapolated sCI. Our work paves the way for future validation of SHDMC applied to challenging 2D materials.
Science & Technology - Other Topics↗
BCS-BEC crossover of the strongly interacting 6 Li − 40 K mixture
Here, we present quantum Monte Carlo calculations of the properties of a two-component mass-imbalanced Fermi gas, corresponding to the 6 Li − 40 K mixture. We compute the equation of state of the unpolarized system as a function of the scattering length with particular attention paid to the unitary limit, where the effect of the effective range of the interaction is explored. In order to investigate differences from the equal-mass case we also compute the pair-distribution function and the momentum distribution over a range of interaction strengths, which can provide information about the structure of the system. Finally, we compute the heavy-light quasiparticle spectrum for the full crossover regime. Our theoretical predictions, based on quantum Monte Carlo calculations, should inform future theoretical studies and can be tested by experiments with ultracold fermionic gases.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Static and dynamic properties of atomic nuclei with high-resolution potentials
Here, we compute ground-state and dynamical properties of 4 He and 16 O nuclei using as input high-resolution, phenomenological nucleon-nucleon and three-nucleon forces that are local in coordinate space. The nuclear Schrodinger equation for both nuclei is accurately solved employing the auxiliary-field diffusion Monte Carlo approach. For the 4 He nucleus, detailed benchmarks are carried out with the hyperspherical harmonics method. In addition to presenting results for the binding energies and radii, we also analyze the momentum distributions of these nuclei and their Euclidean response function corresponding to the isoscalar density transition. The latter quantity is particularly relevant for lepton-nucleus scattering experiments, as it paves the way to quantum Monte Carlo calculations of electroweak response functions of 16 O.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Baryon-baryon, meson-meson, and meson-baryon interactions in nonrelativistic QCD
Van der Waals potentials describing interactions between color-singlet mesons and/or baryons vanish at leading order in potential nonrelativistic quantum chromodynamics (pNRQCD). This result and constraints from Gauss’s law are used to prove that weakly coupled pNRQCD van der Waals potentials in generic non-Abelian gauge theories with only heavy quarks are too weak to form bound states whose color state is a product of color singlets. Quantum Monte Carlo calculations of four, five, and six quarks with equal masses provide numerical evidence that exotic color configurations are higher energy than products of color-singlet hadrons, suggesting that equal-mass fully heavy tetraquark, pentaquark, and hexaquark bound states do not exist at next-to-leading order in pNRQCD and at all orders in QCD-like theories in which all quark masses are asymptotically large. Mechanisms for generating hadron-hadron bound states are identified, which necessarily involve large quark-mass hierarchies, relativistic effects arising from the presence of sufficiently light quarks, or nonperturbative effects outside the scope of weakly coupled pNRQCD.
Effective field theory↗
Emulators for Scarce and Noisy Data: Application to Auxiliary-Field Diffusion Monte Carlo for Neutron Matter
Understanding the equation of state (EOS) of pure neutron matter is necessary for interpreting multimessenger observations of neutron stars. Reliable data analyses of these observations require well-quantified uncertainties for the EOS input, ideally propagating uncertainties from nuclear interactions directly to the EOS. This, however, requires calculations of the EOS for a prohibitively larger number of nuclear Hamiltonians, solving the nuclear many-body problem for each one. Quantum Monte Carlo methods, such as auxiliary-field diffusion Monte Carlo (AFDMC), provide precise and accurate results for the neutron matter EOS, but they are very computationally expensive, making them unsuitable for the fast evaluations necessary for uncertainty propagation. Here, we employ parametric matrix models to develop fast emulators for AFDMC calculations of neutron matter and use them to directly propagate uncertainties of coupling constants in the Hamiltonian to the EOS. As these uncertainties include estimates of the effective field theory truncation uncertainty, this approach provides robust uncertainty estimates for use in astrophysical data analyses. In conclusion, this Letter will enable novel applications such as using astrophysical observations to put constraints on coupling constants for nuclear interactions.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Tomography of Atomic Nuclei
We carry out continuum quantum Monte Carlo calculations of the quantum-mechanical Wigner distribution functions of selected nuclei, up to $^{16}$O. These distributions provide a form of quantum tomography of the spatial and momentum structure of the system. They also help identify the location of high-momentum regions in atomic nuclei and provide insight into the onset of alpha clustering. Besides their intrinsic interest, these distributions will be useful for neutrino event generators, as they correlate the positions and momenta of nucleons in the initial target state. To facilitate their application, we address the need to store them compactly by developing an accurate Gaussian Process emulator that automatically preserves their normalization.
Rocco, Noemi [Valencia U., IFIC; Fermilab]↗
Neutron matter from local chiral effective field theory interactions at large cutoffs
Neutron matter is an important many-body system that provides valuable constraints for the equation of state (EOS) of neutron stars. Neutron-matter calculations employing chiral effective field theory (EFT) interactions have been extensively used for this purpose. Among the various many-body methods, quantum Monte Carlo (QMC) methods stand out due to their nonperturbative nature and the achievable precision. However, QMC methods require local interactions as input, which leads to the appearance of stronger regulator artifacts compared to nonlocal interactions. To circumvent this, we employ large-cutoff interactions derived within chiral EFT (400 MeV ≤ Λ 𝑐 ≤ 700MeV) for studies of pure neutron matter. These interactions have been adjusted to nucleon-nucleon scattering phase shifts, the triton binding energy, as well as the triton 𝛽-decay half-life. We find that regulator artifacts significantly decrease with increasing cutoff, leading to a significant reduction of uncertainties in the neutron-matter EOS. We discuss implications for the symmetry energy and demonstrate how our new calculations lead to a reduction in the theoretical uncertainty of predicted neutron-star radii by up to 30% for low-mass stars.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
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 make 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. Here, 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, the determinant locality approximation, or the determinant T-move schemes, while the older locality approximation 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.
Della Pia, Flaviano [Univ. of Cambridge (United Ki↗
Enhanced stability and ordering of 2D MnBi2Se2Te2
This dataset includes density functional theory and quantum Monte Carlo calculations on MnBi(Se(1-x)Te(x))4 system for its phase stability and defect formation energies. The data supports publication "Increased Defect Resistance and Ordering in MnBi2(Se(1–x)Te(x))4 via Accurate Diffusion Monte Carlo" (https://doi.org/10.1021/acs.jpcc.5c04299).
36 MATERIALS SCIENCE↗
Neural-network quantum states for the nuclear many-body problem
A long-standing goal of nuclear theory is to explain how the structure and dynamics of atomic nuclei and neutron-star matter emerge from the underlying interactions among protons and neutrons. Achieving this goal requires solving the nuclear quantum many-body problem with high accuracy across a wide range of length scales and density regimes. In this review, we discuss how artificial neural network representations of the nuclear many-body wave function have significantly extended the capabilities of continuum quantum Monte Carlo methods. In particular, neural network quantum states enable calculations of larger systems than were previously accessible and provide a flexible framework for capturing phenomena that challenge conventional approaches, including the emergence of nuclear clusters and superfluid phases in dense matter. We highlight recent applications to finite nuclei, infinite nuclear and neutron matter, and dynamical processes relevant to lepton-nucleus and nucleus-nucleus scattering. We also discuss conceptual and methodological connections with condensed matter physics, emphasizing developments in neural network quantum states that bridge strongly correlated systems across disciplines. Together, these developments demonstrate how neural-network methods open new avenues toward unified and accurate descriptions of nuclear structure, matter, and reactions.
Lovato, Alessandro [Argonne; TIFPA-INFN, Trento; V↗
Identifying Band Inversions in Topological Materials Using Diffusion Monte Carlo
Topological insulators are characterized by insulating bulk states and robust metallic surface states. Band inversion is a hallmark of topological insulators. At time-reversal invariant points in the Brillouin zone, spin–orbit coupling (SOC) induces a swapping of orbital character at the bulk band edges. Reliably detecting band inversion in solid-state systems with many-body methods would aid in identifying possible candidates for spintronics and quantum computing applications and improve our understanding of the physics behind topologically nontrivial systems. Density functional theory (DFT) methods are a well-established means of investigating these interesting materials due to their favorable balance of computational cost and accuracy but often struggle to accurately model the electron–electron correlations present in the many materials containing heavier elements. In this work, we develop a novel method to detect band inversion within continuum quantum Monte Carlo (QMC) methods that can accurately treat the electron correlation and spin–orbit coupling that are crucial to the physics of topological insulators. Our approach applies a momentum-space-resolved atomic population analysis throughout the first Brillouin zone utilizing the Löwdin method and the one-body reduced density matrix produced with diffusion Monte Carlo (DMC). We integrate this method into QMCPACK, an open source ab initio QMC package, so that these ground-state methods can be used to complement experimental studies and validate prior DFT work on predicting the band structures of correlated topological insulators. Here, we demonstrate this new technique on the topological insulator bismuth telluride, which displays band inversion between its Bi-p and Te-p states at the Γ-point. We show an increase in charge on the bismuth-p orbital and a decrease in charge on the tellurium-p orbital when comparing band structures with and without SOC. Additionally, we use our method to compare the degree of band inversion present in monolayer Bi 2 Te 3 , which has no interlayer van der Waals interactions, to that seen in the bilayer and bulk. The method presented here will enable future many-body studies of band inversion that can shed light on the delicate interplay between correlation and topology in correlated topological materials.
Band structure↗
Thermodynamic Modeling of Intrinsic Defects in MnBi₂Te₄
This repository contains the computational data supporting the manuscript titled “The critical role of intrinsic defects and many-body interactions on the stability of MnBi₂Te₄.” It includes: 1. DFT data generated using VASP, used for training and benchmarking electronic structure models. 2. Quantum Monte Carlo (QMC) data produced with QMCPACK, used to apply many-body corrections and validate the electronic and magnetic properties of MnBi₂Te₄. 3. Relevant scripts used to run, analyze, and process the calculations, enabling reproducibility and transparency of the workflows.
36 MATERIALS SCIENCE↗
Ab initio electroweak corrections to superallowed β decays and their impact on V ud
Radiative corrections are essential for an accurate determination of V ud from superallowed β decays. In view of recent progress in the single-nucleon sector, the uncertainty is dominated by the theoretical description of nucleus-dependent effects, limiting the precision that can currently be achieved for V ud . In this work, we provide a detailed account of the electroweak corrections to superallowed β decays in effective field theory (EFT), including the power counting, potential and ultrasoft contributions, and factorization in the decay rate. Here, we present a first numerical evaluation of the dominant corrections in light nuclei based on quantum Monte Carlo methods, confirming the expectations from the EFT power counting. Finally, we discuss strategies how to extract from data the low-energy constants that parametrize short-distance contributions and whose values are not predicted by the EFT. Combined with advances in ab initio nuclear-structure calculations, this EFT framework allows one to systematically address the dominant uncertainty in V ud , as illustrated in detail for the 14 O → 14 N transition.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Fluctuating charge-density-wave correlations in the three-band Hubbard model
The high-temperature superconducting cuprates host unidirectional spin- and charge-density-wave orders that can intertwine with superconductivity in nontrivial ways. While the charge components of these stripes have now been observed in nearly all cuprate families, their detailed evolution with doping varies across different materials and at high and low temperatures. We address this problem using nonperturbative determinant quantum Monte Carlo calculations for the three-band Hubbard model. Using an efficient implementation, we can resolve the model’s fluctuating spin and charge modulations and map their evolution as a function of the charge transfer energy and doping. We find that the incommensurability of the charge modulations is decoupled from the spin modulations and decreases with hole doping, consistent with experimental measurements at high temperatures. These findings support the proposal that the high-temperature charge correlations are distinct from the intertwined stripe order observed at low-temperature and in the single-band Hubbard model.
42 ENGINEERING↗
Correlation effects on coupled electronic and structural properties of doped rare-earth trihydrides
Rare-earth trihydride (𝑅H 3 ) compounds exhibit intriguing coupled electronic and structural properties as a function of doping, hydrogen vacancies, and thermodynamic conditions. Theoretical studies of these materials typically rely on density functional theory (DFT), including the use of small supercells that may underestimate strong correlation effects and structural distortions which in turn may influence their metallicity. Here, we elucidate the roles of lattice distortions and correlation effects on the electronic properties of pristine and doped 𝑅H 3 compounds by adopting DFT +U and quantum Monte Carlo (QMC) methods. Linear-response constrained DFT (LR-cDFT) methods find Hubbard U ≈ 2 eV for 𝑅 𝑑 orbitals and U ≈ 6 eV for H 𝑠 /N 𝑝 /O 𝑝 orbitals. The small U on Lu 𝑑 orbitals is consistent with QMC calculations on LuH 3 and LuH 2.875 N 0.125 . In pure face-centered-cubic (FCC) 𝑅H 3 (𝑅 = Lu,Y) compounds, neither DFT nor DFT +U with the self-consistently determined U is enough to create a band gap, however a supercell with hydrogen distortions creates a small gap whose magnitude increases when performing DFT +U with self-consistently determined U values. Furthermore, correlation effects, in turn, have a moderate influence on the coupled structural and electronic properties of doped 𝑅H 3 compounds and may be important when considering the competition between structural distortions and superconductivity.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗