arXiv subjects

D. M. Ceperley

Publications and source records attributed to D. M. Ceperley.

At least 19 recordsLinked to original sources

arXiv2023

Neutral band gap of carbon by quantum Monte Carlo methods

We present a method of calculating the energy gap of a charge-neutral excitation using only ground-state calculations. We report Quantum Monte Carlo calculations of $Γ\rightarrowΓ$ and $Γ\rightarrow X$ particle-hole excitation energies in diamond carbon. We analyze the finite-size effect and find the same $1/L$ decay rate as that in a charged excitation, where $L$ is the linear extension of the supercell. This slow decay is attributed to the delocalized nature of the excitation in supercells too small to accommodate excitonic binding effects. At larger system sizes, the apparent $1/L$ decay crosses over to a $1/L^3$ behavior. Estimation of the scale of exciton binding can be used to correct finite-size effects of neutral gaps.

cond-mat.mtrl-sci↗

arXiv2013

Towards a Predictive First-Principles Description of Solid Molecular Hydrogen with Density-Functional Theory

We examine the influence of the main approximations employed in density-functional theory descriptions of the solid phase of molecular hydrogen near dissociation. We consider the importance of nuclear quantum effects on equilibrium properties and find that they strongly influence intramolecular properties, such as bond fluctuations and stability. We demonstrate that the combination of both thermal and quantum effects make a drastic change to the predicted optical properties of the molecular solid, suggesting a limited value to dynamical, e.g., finite-temperature, predictions based on classical ions and static crystals. We also consider the influence of the chosen exchange--correlation density functional on the predicted properties of hydrogen, in particular, the pressure dependence of the band gap and the zero-point energy. Finally, we use our simulations to make an assessment of the accuracy of typically employed approximations to the calculation of the Gibbs free energy of the solid, namely the quasi-harmonic approximation for solids. We find that, while the approximation is capable of producing free energies with an accuracy of ~10 meV, this is not enough to make reliable predictions of the phase diagram of hydrogen from first-principles due to the small free energy differences seen between several potential structures for the solid; direct free energy calculations for quantum protons are required in order to make definite predictions.

cond-mat.mtrl-sci↗

arXiv2013

Nuclear Quantum Effects and Nonlocal Exchange-Correlation Functionals Applied to Liquid Hydrogen at High Pressure

Using first-principles molecular dynamics, we study the influence of nuclear quantum effects (NQEs) and nonlocal exchange--correlation density functionals (DFs) near molecular dissociation in liquid hydrogen. NQEs strongly influence intramolecular properties, such as bond stability, and are thus an essential part of the dissociation process. Moreover, by including DFs that account for either the self-interaction error or dispersion interactions, we find a much better description of molecular dissociation and metallization than previous studies based on classical protons and/or local or semi-local DFs. We obtain excellent agreement with experimentally measured optical properties along pre-compressed Hugoniots, and while we still find a first-order liquid--liquid transition at low temperatures, transition pressures are increased by more than 100 GPa.

cond-mat.mtrl-sci↗

arXiv2011

The superfluid-insulator transition in the disordered two-dimensional Bose-Hubbard model

We investigate the superfluid-insulator transition in the disordered two-dimensional Bose-Hubbard model through quantum Monte Carlo simulations. The Bose-Hubbard model is studied in the presence of site disorder and the quantum critical point between the Bose-glass and superfluid is determined in both the grand canonical ($μ/U=0.375$ close to $ρ=1$) and canonical ensemble ($ρ=1$ and 0.5). Particular attention is paid to disorder averaging and it is shown that an extremely large number of disorder realizations are needed in order to obtain reliable results. Typically we average over more than $100,000$ disorder realizations. In the grand canonical ensemble we find $Z t_c/U=0.112(1)$ with $μ/U=0.375$, significantly different from previous studies. When compared to the critical point in the absence of disorder ($Z t_c/U=0.2385$), this result confirms previous findings showing that disorder enlarges the superfluid region. At the critical point, in order to estimate universal features, we compute the dynamic conductivity scaling curves.

cond-mat.dis-nn↗

arXiv2011

Validity of the scattering length approximation in strongly interacting Fermi systems

We investigate the energy spectrum of systems of two, three and four spin-1/2 fermions with short range attractive interactions both exactly, and within the scattering length approximation. The formation of molecular bound states and the ferromagnetic transition of the excited scattering state are examined systematically as a function of the 2-body scattering length. Identification of the upper branch (scattering states) is discussed and a general approach valid for systems with many particles is given. We show that an adiabatic ferromagnetic transition occurs, but at a critical transition point kF a much higher than predicted from previous calculations, almost all of which use the scattering length approximation. In the 4-particle system the discrepancy is a factor of 2. The exact critical interaction strength calculated in the 4-particle system is consistent with that reported by experiment. To make comparisons with the adiabatic transition, we study the quench dynamics of the pairing instability using the eigenstate wavefunctions.

cond-mat.quant-gas↗

arXiv2010

Electrical conductivity of high-pressure liquid hydrogen by quantum Monte Carlo methods

We compute the electrical conductivity for liquid hydrogen at high pressure using quantum Monte Carlo. The method uses Coupled Electron-Ion Monte Carlo to generate configurations of liquid hydrogen. For each configuration correlated sampling of electrons is performed in order to calculate a set of lowest many-body eigenstates and current-current correlation functions of the system, which are summed over in the many-body Kubo formula to give AC electrical conductivity directly. The extrapolated DC conductivity at 3000 K for several densities shows a liquid semiconductor to liquid-metal transition at high pressure. Our results are in good agreement with shock-wave data.

cond-mat.str-el↗

arXiv2009

Construction of localized wave functions for a disordered optical lattice and analysis of the resulting Hubbard model parameters

We propose a method to construct localized single particle wave functions using imaginary time projection and thereby determine lattice Hamiltonian parameters. We apply the method to a specific disordered potential generated by an optical lattice experiment and calculate for each instance of disorder, the equivalent lattice model parameters. The probability distributions of the Hubbard parameters are then determined. Tests of localization and eigen-energy convergence are examined.

cond-mat.dis-nn↗

arXiv2009

Hexatic and mesoscopic phases in the 2D quantum Coulomb system

We study the Wigner crystal melting in a two dimensional quantum system of particles interacting via the 1/r Coulomb potential. We use quantum Monte Carlo methods to calculate its phase diagram, locate the Wigner crystal region, and analyze its instabilities towards the liquid phase. We discuss the role of quantum effects in the critical behavior of the system, and compare our numerical results with the classical theory of melting, and the microemulsion theory of frustrated Coulomb systems. We find a Pomeranchuk effect much larger then in solid helium. In addition, we find that the exponent for the algebraic decay of the hexatic phase differs significantly from the Kosterilitz-Thouless theory of melting. We search for the existence of mesoscopic phases and find evidence of metastable bubbles but no mesoscopic phase that is stable in equilibrium.

cond-mat.str-el↗

arXiv2009

Phase separation in hydrogen-helium mixtures at Mbar pressures

The properties of hydrogen-helium mixtures at Mbar pressures and intermediate temperatures (4000 to 10000 K) are calculated with first-principles molecular dynamics simulations. We determine the equation of state as a function of density, temperature, and composition and, using thermodynamic integration, we estimate the Gibbs free energy of mixing, thereby determining the temperature, at a given pressure, when helium becomes insoluble in dense metallic hydrogen. These results are directly relevant to models of the interior structure and evolution of Jovian planets. We find that the temperatures for the demixing of helium and hydrogen are sufficiently high to cross the planetary adiabat of Saturn at pressures around 5 Mbar; helium is partially miscible throughout a significant portion of the interior of Saturn, and to a lesser extent in Jupiter.

cond-mat.mtrl-sci↗

arXiv2008

Exact quantum Monte Carlo study of one dimensional trapped fermions with attractive contact interactions

Using exact continuous quantum Monte Carlo techniques, we study the zero and finite temperature properties of a system of harmonically trapped one dimensional spin 1/2 fermions with short range interactions. Motivated by experimental searches for modulated Fulde-Ferrel-Larkin-Ovchinikov states, we systematically examine the impact of a spin imbalance on the density profiles. We quantify the accuracy of the Thomas-Fermi approximation, finding that for sufficiently large particle numbers (N > 100) it quantitatively reproduces most features of the exact density profile. The Thomas-Fermi approximation fails to capture small Friedel-like spin and density oscillations and overestimates the size of the fully paired region in the outer shell of the trap. Based on our results, we suggest a range of experimentally tunable parameters to maximize the visibility of the double shell structure of the system and the Fulde-Ferrel-Larkin-Ovchinikov state in the one dimensional harmonic trap. Furthermore, we analyze the fingerprints of the attractive contact interactions in the features of the momentum and pair momentum distributions.

cond-mat.other↗

arXiv2007

The Hartree-Fock ground state of the three-dimensional electron gas

In 1962, Overhauser showed that within Hartree-Fock (HF) the electron gas is unstable to a spin density wave (SDW) instability. Determining the true HF ground state has remained a challenge. Using numerical calculations for finite systems and analytic techniques, we study the HF ground state of the 3D electron gas. At high density, we find broken spin symmetry states with a nearly constant charge density. Unlike previously discussed spin wave states, the observed wave vector of the SDW is smaller than $2 k_F$. The broken-symmetry state originates from pairing instabilities at the Fermi surface, a model for which is proposed.

cond-mat.str-el↗

arXiv2006

Theory of Small Para-Hydrogen Clusters: Magic Numbers and Superfluid Sizes

The interplay between magic number stabilities and superfluidity of small para-hydrogen clusters with sizes $N = 5$ to 40 and temperatures $0.5 K \leq T \leq 4.5 $K is explored with classical and quantum Path Integral Monte Carlo calculations. Clusters with $N < 26$ and T $\leq 1.5 K$ have large superfluid fractions even at the stable magic numbers 13, 19, and 23. In larger clusters, superfluidity is quenched especially at the magic numbers 23, 26, 29, 32, and 37 while below 1 K, superfluidity is recovered for the pairs $(27,28)$, $(30,31)$, and $(35,36)$. For all clusters superfluidity is localized at the surface and correlates with long exchange cycles involving loosely bound surface molecules.

physics.comp-ph↗

arXiv2006

Quantum Monte Carlo Simulation of the High-Pressure Molecular-Atomic Crossover in Fluid Hydrogen

A first-order liquid-liquid phase transition in high-pressure hydrogen between molecular and atomic fluid phases has been predicted in computer simulations using ab initio molecular dynamics approaches. However, experiments indicate that molecular dissociation may occur through a continuous crossover rather than a first-order transition. Here we study the nature of molecular dissociation in fluid hydrogen using an alternative simulation technique in which electronic correlation is computed within quantum Monte Carlo, the so-called Coupled Electron Ion Monte Carlo (CEIMC) method. We find no evidence for a first-order liquid-liquid phase transition.

cond-mat.stat-mech↗

arXiv2006

Many-body wavefunctions for normal liquid $^3$He

We present new trial wave-functions which include 3-body correlations into the backflow coordinates and a 4-body symmetric potential. We show that our wavefunctions lower the energy enough to stabilize the ground state energies of normal liquid $^3$He in the unpolarized state at all pressures in agreement with experiment; however, quantitative discrepancies remain. Further, we include strong spin coupling into the Fermi liquid by adapting pairing wave functions. We demonstrate a new, numerically stable method to evaluate pairing functions which is also useful for Path Integrals calculations at low, but non-zero temperatures.

cond-mat.str-el↗

arXiv2006

Pairing and Superfluid Properties of Dilute Fermion Gases at Unitarity

We study the system of a dilute gas of fermions in 3-dimensions, with attractive interactions tuned to the unitarity point, using the non-perturbative Restricted Path Integral Monte Carlo (R-PIMC) method. The pairing and superfluid properties of this system are calculated at finite temperature. The total energy at very low temperature from our results agrees closely with that of previous ground-state Quantum Monte Carlo calculations. We identify the temperature $T^\ast\approx 0.70ε_F$ below which pairing correlations develop, and estimate the critical temperature for the superfluid transition $T_c\approx 0.25ε_F$ from a finite size scaling analysis of the superfluid density.

cond-mat.stat-mech↗

arXiv2005

Off-Diagonal Long-Range Order in Solid 4He

Measurements of the moment of inertia by Kim and Chan have found that solid 4He acts like a supersolid at low temperatures. To understand the order in solid 4He, we have used Path Integral Monte Carlo to calculate the off-diagonal long range order (ODLRO) (equivalent to Bose-Einstein condensation, BEC). We do not find ODLRO in a perfect hcp crystal at the melting density. We discuss these results in relation to proposed quantum solid trial functions. We conclude that the solid 4He wave function has correlations which suppress both vacancies and BEC.

cond-mat.other↗

arXiv2005

Superfluidity of Dense $^4$He in Vycor

We calculate properties of a model of $^4$He in Vycor using the Path Integral Monte Carlo method. We find that $^4$He forms a distinct layered structure with a highly localized first layer, a disordered second layer with some atoms delocalized and able to give rise to the observed superfluid response, and higher layers nearly perfect crystals. The addition of a single $^3$He atom was enough to bring down the total superfluidity by blocking the exchange in the second layer. Our results are consistent with the persistent liquid layer model to explain the observations. Such a model may be relevant to the experiments on bulk solid $^4$He, if there is a fine network of grain boundaries in those systems.

physics.comp-ph↗

arXiv2005

Path Integral Calculations of exchange in solid 4He

Recently there have been experimental indications that solid 4He might be a supersolid. We discuss the relation of supersolid behavior to ring exchange. The tunnelling frequencies for ring exchanges in quantum solids are calculated using Path Integral Monte Carlo by finding the free energy for making a path that begins with the atoms in one configuration and ends with a permutation of those positions. We find that the exchange frequencies in solid 4He are described by a simple lattice model which does not show supersolid behavior. Thus, the PIMC calculations constrain the mechanism for the supersolid behavior. We also look at the characteristics of very long exchanges needed for macroscopic mass transport.

cond-mat.other↗