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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Electronic energy gap closure and metal-insulator transition in dense liquid hydrogen

Here, using quantum Monte Carlo (QMC) calculations, we investigate the insulator-metal transition observed in liquid hydrogen at high pressure. Below the critical temperature of the transition from the molecular to the atomic liquid, the fundamental electronic gap closure occurs abruptly, with a small discontinuity reflecting the weak first-order transition in the thermodynamic equation of state. Above the critical temperature, molecular dissociation sets in while the gap is still open. When the gap closes, the decay of the off-diagonal reduced density matrix shows that the liquid enters a gapless, but localized, phase: there is a crossover between the insulating and the metallic liquids. Compared to different density functional theory (DFT) functionals, our QMC calculations provide larger values for the fundamental gap and the electronic density of states close to the band edges, indicating that optical properties from DFT potentially benefit from error cancellations.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Diffusion Monte Carlo approaches for studying nuclear quantum effects in fluxional molecules

Abstract Diffusion quantum Monte Carlo (DMC) provides a powerful approach for obtaining the ground state energy and wave function of molecules, ions, and molecular clusters. The approach is uniquely well suited for studies of fluxional molecules, which undergo large amplitude vibrational motions even in their ground state. In contrast to the electronic structure problem, where the wave function must be antisymmetric with respect to exchange of any pair of electrons, the wave function for the ground vibrational state is nodeless. This greatly simplifies the application of DMC for vibrational problems. Because there is not a single potential function that can be used to describe the intramolecular and intermolecular interactions in all molecular systems, most methods that are used to describe nuclear quantum effects rely on a carefully chosen zero‐order description of the molecular vibrations. In contrast, DMC calculations can be performed in Cartesian coordinates, making the DMC algorithm easily transferable between different chemical systems. In this contribution, the theory that underlies DMC will be discussed along with important considerations for performing DMC calculations. Extensions for evaluating vibrationally excited states and molecular properties are also discussed. Insights that can be obtained from DMC calculations are illustrated in the context of the protonated water clusters. This article is categorized under: Molecular and Statistical Mechanics > Molecular Dynamics and Monte‐Carlo Methods Theoretical and Physical Chemistry > Spectroscopy

Chemistry↗
DOE OSTI2025

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 ↗
DOE OSTI2024

Magnetic, charge, and bond order in the two-dimensional Su-Schrieffer-Heeger-Holstein model

Most nonperturbative numerical studies of electron-phonon interactions focus on model Hamiltonians where the electrons interact with a phonon branch via a single type of microscopic mechanism. Two commonly explored couplings in this context are the Holstein and Su-Schrieffer-Heeger (SSH) interactions, which describe phonons modulating the on-site energy and intersite electron hopping, respectively. Many materials, however, have multiple phonon branches that can each interact with electronic degrees of freedom in different ways. We present here a determinant quantum Monte Carlo study of the half-filled two-dimensional (bond) SSH-Holstein Hamiltonian, where electrons couple to different phonon branches via either the Holstein or SSH mechanism. As a result, we map the model's phase diagram and determine the nature of the transitions between charge-density wave, bond-order wave, and antiferromagnetic order.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Kekulé valence bond order in the honeycomb lattice optical Su-Schrieffer-Heeger model and its relevance to graphene

We perform sign-problem-free determinant quantum Monte Carlo simulations of the optical Su- Schrieffer-Heeger model on a half-filled honeycomb lattice. In particular, we investigate the model’s semi-metal (SM) to Kekulé Valence Bond Solid (KVBS) phase transition at zero and finite temper- atures as a function of phonon energy and interaction strength. Using hybrid Monte Carlo sampling methods we can simulate the model near the adiabatic regime, allowing us to access regions of parameter space relevant to graphene. Our simulations suggest that the SM-KVBS transition is weakly first-order at all temperatures, with graphene situated close to the phase boundary in the SM region of the phase diagram. Furthermore, our results highlight the important role bond-stretching phonon modes play in the formation of KVBS order in strained graphene-derived systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Interaction-expansion inchworm Monte Carlo solver for lattice and impurity models

Multiorbital quantum impurity models with general interaction and hybridization terms appear in a wide range of applications, including embedding, quantum transport, and nanoscience. However, most quantum impurity solvers are restricted to a few impurity orbitals, discretized baths, diagonal hybridizations, or density-density interactions. We generalize the inchworm quantum Monte Carlo method to the interaction expansion, and we explore its application to typical single- and multiorbital problems encountered in investigations of impurity and lattice models. Our implementation generically outperforms bare and bold-line quantum Monte Carlo algorithms in the interaction expansion. For the systems studied here, our implementation remains inferior to the more specialized hybridization expansion and auxiliary field algorithms. So, the problem of convergence to unphysical fixed points, which hampers so-called bold-line methods, is not encountered in inchworm Monte Carlo.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Denoising of imaginary time response functions with Hankel projections

Imaginary-time response functions of finite-temperature quantum systems are often obtained with methods that exhibit stochastic or systematic errors. Reducing these errors comes at a large computational cost—in quantum Monte Carlo simulations, the reduction of noise by a factor of two incurs a simulation cost of a factor of four. In this paper, we relate certain imaginary-time response functions to an inner product on the space of linear operators on Fock space. We then show that data with noise typically does not respect the positive definiteness of its associated Gramian. The Gramian has the structure of a Hankel matrix. As a method for denoising noisy data, we introduce an alternating projection algorithm that finds the closest positive definite Hankel matrix consistent with noisy data. We test our methodology at the example of fermion Green's functions for continuous-time quantum Monte Carlo data and show remarkable improvements of the error, reducing noise by a factor of up to 20 in practical examples. We argue that Hankel projections should be used whenever finite-temperature imaginary-time data of response functions with errors is analyzed, be it in the context of quantum Monte Carlo, quantum computing, or in approximate semianalytic methodologies. Published by the American Physical Society 2024

Yu, Yang (ORCID:0000000186178878)↗
DOE OSTI2020

The role of high-order electron correlation effects in a model system for non-valence correlation-bound anions

The diffusion Monte Carlo (DMC), auxiliary field quantum Monte Carlo (AFQMC), and equation-of-motion coupled cluster (EOM-CC) methods are used to calculate the electron binding energy (EBE) of the non-valence anion state of a model (H2O)4 cluster. Two geometries are considered, one at which the anion is unbound and the other at which it is bound in the Hartree–Fock (HF) approximation. It is demonstrated that DMC calculations can recover from the use of a HF trial wave function that has collapsed onto a discretized continuum solution, although larger EBEs are obtained when using a trial wave function for the anion that provides a more realistic description of the charge distribution and, hence, of the nodal surface. For the geometry at which the cluster has a non-valence correlation-bound anion, both the inclusion of triples in the EOM-CC method and the inclusion of supplemental diffuse d functions in the basis set are important. DMC calculations with suitable trial wave functions give EBE values in good agreement with our best estimate EOM-CC result. AFQMC using a trial wave function for the anion with a realistic electron density gives a value of the EBE nearly identical to the EOM-CC result when using the same basis set. For the geometry at which the anion is bound in the HF approximation, the inclusion of triple excitations in the EOM-CC calculations is much less important. The best estimate EOM-CC EBE value is in good agreement with the results of DMC calculations with appropriate trial wave functions.

Upadhyay, Shiv (ORCID:0000000285010501)↗
DOE OSTI2020

Doping a bad metal: Origin of suppression of the metal-insulator transition in nonstoichiometric VO 2

Rutile ( R ) phase VO 2 is a quintessential example of a strongly correlated bad metal, which undergoes a metal-insulator transition (MIT) concomitant with a structural transition to a V-V dimerized monoclinic ( M 1 ) phase below T MIT ~ 340 K . It has been experimentally illustrated that one can control this transition by doping VO 2 . In particular, doping with oxygen vacancies ( V O ) has been shown to completely suppress this MIT without any structural transition. We explain this suppression by elucidating the influence of oxygen vacancies on the electronic structure of the metallic R phase VO 2 , explicitly treating strong electron-electron correlations using dynamical mean-field theory (DMFT) as well as diffusion Monte Carlo (DMC) flavor of quantum Monte Carlo (QMC) techniques. DMC calculations show a gap closure in the M 1 phase when vacancies are present, suggesting that when vacancies are introduced in the high-temperature rutile phase, the dimerized insulating phase cannot be reached when temperature is lowered. Both DMFT and DMC calculations of nonstoichiometric metallic rutile phase shows that this tendency not to dimerize in the presence of vacancies is because V O 's tend to change the V - 3 d filling away from its nominal half-filled value, with the e g π orbitals competing with the otherwise dominant a 1 g orbital. Loss of this near orbital polarization of the a 1 g orbital is associated with a weakening of electron correlations, especially along the V-V dimerization direction. This removes a charge-density wave (CDW) instability along this direction above a critical doping concentration, which further suppresses the metal-insulator transition. Our research further suggests that the MIT is predominantly driven by a correlation-induced CDW instability along the V-V dimerization direction.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Zero-point motion of liquid and solid hydrogen

We present an inelastic neutron scattering study of liquid and solid hydrogen carried out using the wide Angular Range Chopper Spectrometer at Oak Ridge National Laboratory. From the observed dynamic structure factor, we obtained empirical estimates of the molecular mean-squared displacement and average translational kinetic energy. Here we find that the former quantity increases with temperature, indicating that a combination of thermal and quantum effects is important near the liquid-solid phase transition, contrary to previous measurements. We also find that the kinetic energy drops dramatically on melting of the crystals, a consequence of the large increase in molar volume together with the Heisenberg indeterminacy principle. Our results are compared with quantum Monte Carlo simulations based on different model potentials. In general, there is good agreement between our findings and theoretical predictions based on the Silvera-Goldman and Buck potentials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Bilayer Hubbard model: Analysis based on the fermionic sign problem

The bilayer Hubbard model describes the antiferromagnet to spin singlet transition and, potentially, aspects of the physics of unconventional superconductors. Despite these important applications, significant aspects of its phase diagram in the interplane hopping t ⊥ versus on-site interaction U parameter space, at half filling, are largely in disagreement. Here we provide an analysis making use of the average sign of weights over the course of the importance sampling in quantum Monte Carlo simulations to resolve several central open questions. Specifically, this metric of the weights clarifies the finite-sized metallic regimes at small U. Furthermore, at strong interactions, it points to the existence of a crossover from a correlated to uncorrelated band insulator not yet explored in a variety of existing, unbiased numerical methods. Our paper demonstrates the versatility of using properties of the weights in quantum Monte Carlo simulations to reveal important physical characteristics of the models under study.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Stripe correlations in the two-dimensional Hubbard-Holstein model

Several state-of-the-art numerical methods have observed static or fluctuating spin and charge stripes in doped two-dimensional Hubbard models, suggesting that these orders play a significant role in shaping the cuprate phase diagram. Many experiments, however, also indicate that the cuprates have strong electron-phonon (e-ph) coupling, and it is unclear how this interaction influences stripe correlations. We study static and fluctuating stripe orders in the doped single-band Hubbard-Holstein model using zero temperature variational Monte Carlo and finite temperature determinant quantum Monte Carlo. We find that the lattice couples more strongly with the charge component of the stripes, leading to an enhancement or suppression of stripe correlations, depending on model parameters like the next-nearest-neighbor hopping t' or phonon energy Ω. Our results help elucidate how the e-ph interaction can tip the delicate balance between stripe and superconducting correlations in the Hubbard-Holstein model with implications for our understanding of the high-T c cuprates.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Matrix-Model Simulations Using Quantum Computing, Deep Learning, and Lattice Monte Carlo

Matrix quantum mechanics plays various important roles in theoretical physics, such as a holographic description of quantum black holes, and it underpins the only practical numerical approach to the study of complex high-dimensional supergravity theories. Understanding quantum black holes and the role of entanglement in a holographic setup is of paramount importance for the realization of a quantum theory of gravity. Moreover, a complete numerical understanding of the holographic duality and the emergence of geometric space-time features from microscopic degrees of freedom could pave the way for new discoveries in quantum information science. Euclidean lattice Monte Carlo simulations are the de facto numerical tool for understanding the spectrum of large matrix models and have been used to test the holographic duality. However, they are not tailored to extract dynamical properties or even the quantum wave function of the ground state of matrix models. Quantum computing and deep learning provide potentially useful approaches to study the dynamics of matrix quantum mechanics. If successful in the context of matrix models, these rapidly improving numerical techniques could become the new Swiss army knife of quantum gravity practitioners. In this paper, we perform the first systematic survey for quantum computing and deep-learning approaches to matrix quantum mechanics, comparing them to lattice Monte Carlo simulations. These provide baseline benchmarks before addressing more complicated problems. In particular, we test the performance of each method by calculating the low-energy spectrum.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Explicitly antisymmetrized neural network layers for variational Monte Carlo simulation

The combination of neural networks and quantum Monte Carlo methods has arisen as a promising path forward for highly accurate electronic structure calculations. Previous proposals have combined equivariant neural network layers with a final antisymmetric layer in order to satisfy the antisymmetry requirements of the electronic wavefunction. However, to date it is unclear if one can represent antisymmetric functions of physical interest, and it is difficult to precisely measure the expressiveness of the antisymmetric layer. Here, this work attempts to address this problem by introducing explicitly antisymmetrized universal neural network layers. This approach has a computational cost which increases factorially with respect to the system size, but we are nonetheless able to apply it to small systems to better understand how the structure of the antisymmetric layer affects its performance. We first introduce a generic antisymmetric (GA) neural network layer, which we use to replace the entire antisymmetric layer of the highly accurate ansatz known as the FermiNet. We demonstrate that the resulting FermiNet-GA architecture can yield effectively the exact ground state energy for small atoms and molecules. We then consider a factorized antisymmetric (FA) layer which more directly generalizes the FermiNet by replacing the products of determinants with products of antisymmetrized neural networks. We find, interestingly, that the resulting FermiNet-FA architecture does not significantly outperform the FermiNet. This strongly suggests that the sum of products of antisymmetries is a key limiting aspect of the FermiNet architecture. To explore this further, we investigate a slight modification of the FermiNet, called the full determinant mode, which replaces each product of determinants with a single combined determinant. We find that the full single-determinant FermiNet closes a large part of the gap between the standard single-determinant FermiNet and FermiNet-GA on small atomic and molecular problems. Surprisingly, on the nitrogen molecule at a dissociating bond length of 4.0 Bohr, the full single-determinant FermiNet can outperform the largest standard FermiNet calculation with 64 determinants.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Hamming distance and the onset of quantum criticality

Simulating models for quantum correlated matter unveils the inherent limitations of deterministic classical computations. In particular, in the case of quantum Monte Carlo methods, this is manifested by the emergence of negative weight configurations in the sampling, that is, the sign problem (SP). There have been several recent calculations which exploit the SP to locate underlying critical behavior. Here, utilizing a metric that quantifies phase-space ergodicity in such sampling, the Hamming distance, we suggest a significant advance on these ideas to extract the location of quantum critical points in various fermionic models, in spite of the presence of a severe SP. Combined with other methods, exact diagonalization in our case, it elucidates both the nature of the different phases as well as their location, as we demonstrate explicitly for the honeycomb and triangular Hubbard models, in both their U(1) and SU(2) forms. Furthermore, our approach exemplifies a possible path allowing the exploration of the phase diagram of a variety of fermionic quantum models hitherto considered to be impractical via quantum Monte Carlo simulations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

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↗
DOE OSTI2022

Quantum Markov chain Monte Carlo with digital dissipative dynamics on quantum computers

Modeling the dynamics of a quantum system connected to the environment is critical for advancing our understanding of complex quantum processes, as most quantum processes in nature are affected by an environment. Modeling a macroscopic environment on a quantum simulator may be achieved by coupling independent ancilla qubits that facilitate energy exchange in an appropriate manner with the system and mimic an environment. This approach requires a large, and possibly exponential number of ancillary degrees of freedom which is impractical. In contrast, we develop a digital quantum algorithm that simulates interaction with an environment using a small number of ancilla qubits. By combining periodic modulation of the ancilla energies, or spectral combing, with periodic reset operations, we are able to mimic interaction with a large environment and generate thermal states of interacting many-body systems. We evaluate the algorithm by simulating preparation of thermal states of the transverse Ising model. Our algorithm can also be viewed as a quantum Markov chain Monte Carlo process that allows sampling of the Gibbs distribution of a multivariate model. To illustrate this we evaluate the accuracy of sampling Gibbs distributions of simple probabilistic graphical models using the algorithm.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

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↗