arXiv subjects

Markus Holzmann

Publications and source records attributed to Markus Holzmann.

At least 91 records · Page 5Linked to original sources

arXiv2016

Theory of Finite Size Effects for Electronic Quantum Monte Carlo Calculations of Liquids and Solids

Concentrating on zero temperature Quantum Monte Carlo calculations of electronic systems, we give a general description of the theory of finite size extrapolations of energies to the thermodynamic limit based on one and two-body correlation functions. We introduce new effective procedures, such as using the potential and wavefunction split-up into long and short range functions to simplify the method and we discuss how to treat backflow wavefunctions. Then we explicitly test the accuracy of our method to correct finite size errors on example hydrogen and helium many-body systems and show that the finite size bias can be drastically reduced for even small systems.

physics.comp-ph↗

arXiv2015

Approximation of Schrödinger operators with $δ$-interactions supported on hypersurfaces

We show that a Schrödinger operator $A_{δ, α}$ with a $δ$-interaction of strength $α$ supported on a bounded or unbounded $C^2$-hypersurface $Σ\subset \mathbb{R}^d$, $d\ge 2$, can be approximated in the norm resolvent sense by a family of Hamiltonians with suitably scaled regular potentials. The differential operator $A_{δ, α}$ with a singular interaction is regarded as a self-adjoint realization of the formal differential expression $-Δ- α\langle δ_Σ, \cdot \rangle δ_Σ$, where $α\colonΣ\rightarrow \mathbb{R}$ is an arbitrary bounded measurable function. We discuss also some spectral consequences of this approximation result.

math.SP↗

arXiv2015

Benchmarking Hydrogen-Helium Mixtures with QMC: Energetics, Pressures, and Forces

An accurate understanding of the phase diagram of dense hydrogen and helium mixtures is a crucial component in the construction of accurate models of Jupiter, Saturn, and Jovian extrasolar planets. Though DFT based first principles methods have the potential to provide the accuracy and computational efficiency required for this task, recent benchmarking in hydrogen has shown that achieving this accuracy requires a judicious choice of functional, and a quantification of the errors introduced. In this work, we present a quantum Monte Carlo based benchmarking study of a wide range of density functionals for use in hydrogen-helium mixtures at thermodynamic conditions relevant for Jovian planets. Not only do we continue our program of benchmarking energetics and pressures, but we deploy QMC based force estimators and use them to gain insights into how well the local liquid structure is captured by different density functionals. We find that TPSS, BLYP and vdW-DF are the most accurate functionals by most metrics, and that the enthalpy, energy, and pressure errors are very well behaved as a function of helium concentration. Beyond this, we highlight and analyze the major error trends and relative differences exhibited by the major classes of functionals, and estimate the magnitudes of these effects when possible.

cond-mat.mtrl-sci↗

arXiv2015

Iterative backflow renormalization procedure for many-body ground state wave functions of strongly interacting normal Fermi liquids

We show how a ground state trial wavefunction of a Fermi liquid can be systematically improved introducing a sequence of renormalized coordinates through an iterative backflow transformation. We apply this scheme to calculate the ground state energy of liquid $^3$He in two dimensions at freezing density using variational and fixed-node diffusion Monte Carlo. Comparing with exact transient estimate results for systems with small number of particles, we find that variance extrapolations provide accurate results for the true ground state together with stringent lower bounds. For larger systems these bounds can in turn be used to quantify the systematic bias of fixed-node calculations. These wave functions are size consistent and the scaling of their computational complexity with the number of particles is the same as for standard backflow wave functions.

cond-mat.str-el↗

arXiv2014

Molecular-Atomic Transition in the Deuterium Hugoniot with Coupled Electron Ion Monte Carlo

We have performed accurate simulations of the Deuterium Hugoniot using Coupled Electron Ion Monte Carlo (CEIMC). Using highly accurate quantum Monte Carlo methods for the electrons, we study the region of maximum compression along the principal Hugoniot, where the system undergoes a continuous transition from a molecular fluid to a monatomic fluid. We include all relevant physical corrections so that a direct comparison to experiment can be made. Around 50 GPa we found a maximum compression of 4.85, roughly 10% larger than previous theoretical predictions and experimental data but still compatible with the latter because of their large uncertainty.

cond-mat.str-el↗

arXiv2013

Hartree-Fock Ground State Phase Diagram of Jellium

We calculate the ground state phase diagram of the homogeneous electron gas in three dimensions within the Hartree-Fock approximation and show that broken symmetry states are energetically favored at any density against the homogeneous Fermi gas state with isotropic Fermi surface. At high density, we find metallic spin-unpolarized solutions where electronic charge and spin density form an incommensurate crystal having more crystal sites than electrons. For $r_s \to 0$, our solutions approach pure spin-density waves, whereas the commensurate Wigner crystal is favored at lower densities, $r_s > 3.4$. Decreasing the density, the system undergoes several structural phase transitions with different lattice symmetries. The polarization transition occurs around $r_s \approx 8.5$.

cond-mat.str-el↗

arXiv2013

Universal Superfluid Transition and Transport Properties of Two-Dimensional Dirty Bosons

We study the phase diagram of two-dimensional, interacting bosons in the presence of a correlated disorder in continuous space, using large-scale finite temperature quantum Monte Carlo simulations. We show that the superfluid transition is strongly protected against disorder. It remains of the Berezinskii-Kosterlitz-Thouless type up to disorder strengths comparable to the chemical potential. Moreover, we study the transport properties in the strong disorder regime where a zero-temperature Bose-glass phase is expected. We show that the conductance exhibits a thermally activated behavior vanishing only at zero temperature. Our results point towards the existence of Bose bad-metal phase as a precursor of the Bose-glass phase.

cond-mat.quant-gas↗

arXiv2013

Exchange-correlation energy for the 3D homogeneous electron gas at arbitrary temperature

We fit finite-temperature path integral Monte Carlo calculations of the exchange-correlation energy of the 3D finite-temperature homogeneous electron gas in the warm-dense regime (r_{s} = (3/4πn)^{1/3} a_{B}^{-1} < 40 and Θ= T/T_{F} > 0.0625). In doing so, we construct a Padé approximant which collapses to Debye-Hückel theory in the high-temperature, low-density limit. Likewise, the zero-temperature limit matches the numerical results of ground-state quantum Monte Carlo, as well as analytical results in the high-density limit.

cond-mat.str-el↗

arXiv2012

Momentum distribution and Compton profile by the ab initio GW approximation

We present two possible approaches to calculate the momentum distribution n(p) and the Compton profile within the framework of the ab initio GW approximation on the self-energy. The approaches are based on integration of the Green's function along either the real or the imaginary axes. Examples will be presented on the jellium model and on real bulk sodium. Advantages and drawbacks of both methods are discussed in comparison with accurate quantum Monte Carlo (QMC) calculations and x-ray Compton scattering experiments. We illustrate the effect of many-body correlations and disentangle them from band-structure and anisotropy effects by a comparison with density functional theory in the local density approximation. Our results suggest the use of G0W0 momentum distributions as reference for future experiments and theory developments.

cond-mat.other↗

arXiv2012

Effect of disorder close to the superfluid transition in a two-dimensional Bose gas

We experimentally study the effect of disorder on trapped quasi two-dimensional (2D) 87Rb clouds in the vicinity of the Berezinskii-Kosterlitz-Thouless (BKT) phase transition. The disorder correlation length is of the order of the Bose gas characteristic length scales (thermal de Broglie wavelength, healing length) and disorder thus modifies the physics at a microscopic level. We analyze the coherence properties of the cloud through measurements of the momentum distributions, for two disorder strengths, as a function of its degeneracy. For moderate disorder, the emergence of coherence remains steep but is shifted to a lower entropy. In contrast, for strong disorder, the growth of coherence is hindered. Our study is an experimental realization of the dirty boson problem in a well controlled atomic system suitable for quantitative analysis.

cond-mat.quant-gas↗

arXiv2011

Condensed Fraction of an Atomic Bose Gas Induced by Critical Correlations

We study the condensed fraction of a harmonically-trapped atomic Bose gas at the critical point predicted by mean-field (MF) theory. The non-zero condensed fraction $f_0$ is induced by critical correlations which increase the transition temperature $T_c$ above $\T_c^{MF}$. Unlike the $T_c$ shift in a trapped gas, $f_0$ is sensitive only to the critical behaviour in the quasi-uniform part of the cloud near the trap centre. To leading order in the interaction parameter $a/λ_0$, where $a$ is the s-wave scattering length and $λ_0$ the thermal wavelength, we expect a universal scaling $f_0 \propto (a/λ_0)^4$. We experimentally verify this scaling using a Feshbach resonance to tune $a/λ_0$. Further, using the local density approximation, we compare our measurements with the universal result obtained from Monte-Carlo simulations for a uniform system, and find excellent quantitative agreement.

cond-mat.quant-gas↗

arXiv2011

The momentum distribution of the homogeneous electron gas

We calculate the off-diagonal density matrix of the homogeneous electron gas at zero temperature using unbiased Reptation Monte Carlo for various densities and extrapolate the momentum distribution, and the kinetic and potential energies to the thermodynamic limit. Our results on the renormalization factor allows us to validate approximate G_0W_0 calculations concerning quasiparticle properties over a broad density region (1 <= r_s <= 10) and show that near the Fermi surface, vertex corrections and self-consistency aspects almost cancel each other out.

cond-mat.str-el↗

arXiv2011

Finite-size analysis of the Fermi liquid properties of the homogeneous electron gas

We analyze the extrapolation to the thermodynamic limit of Fermi liquid properties of the homogeneous electron gas in two and three dimensions. Using field theory, we explicitly calculate finite-size effects of the total energy, the renormalization factor, and the effective mass at the Fermi surface within the random phase approximation (RPA) and discuss the validity for general metallic systems.

cond-mat.str-el↗

arXiv2010

High-energy excitonic effects in graphite and graphene

We present ab initio many-body calculations of the optical absorption in bulk graphite, graphene and bilayer of graphene. Electron-hole interaction is included solving the Bethe-Salpeter equation on top of a GW quasiparticle electronic structure. For all three systems, we observe strong excitonic effects at high energy, well beyond the continuum of π-> π* transitions. In graphite, these affect the onset of σ-> σ* transitions. In graphene, we predict an excitonic resonance at 8.3 eV arising from a background continuum of dipole forbidden transitions. In the graphene bilayer, the resonance is shifted to 9.6 eV. Our results for graphite are in good agreement with experiments.

cond-mat.mtrl-sci↗

arXiv2010

Momentum Distribution and Renormalization Factor in Sodium and the Electron Gas

We present experimental and theoretical results on the momentum distribution and the quasiparticle renormalization factor in sodium. From an x-ray Compton-profile measurement of the valence-electron momentum density, we derive its discontinuity at the Fermi wavevector. This yields an accurate measure of the renormalization factor that we compare with quantum Monte Carlo and GW calculations performed both on crystalline sodium and on the homogeneous electron gas. Our calculated results are in good agreement with the experiment.

cond-mat.other↗

arXiv2010

The equilibrium state of a trapped two-dimensional Bose gas

We study experimentally and numerically the equilibrium density profiles of a trapped two-dimensional $^{87}$Rb Bose gas, and investigate the equation of state of the homogeneous system using the local density approximation. We find a clear discrepancy between in-situ measurements and Quantum Monte Carlo simulations, which we attribute to a non-linear variation of the optical density of the atomic cloud with its spatial density. However, good agreement between experiment and theory is recovered for the density profiles measured after time-of-flight, taking advantage of their self-similarity in a two-dimensional expansion.

cond-mat.quant-gas↗

arXiv2009

Universal correlations and coherence in quasi-two-dimensional trapped Bose gases

We study the quasi-two-dimensional Bose gas in harmonic traps at temperatures above the Kosterlitz-Thouless transition, where the gas is in the normal phase. We show that mean-field theory takes into account the dominant interaction effects for experimentally relevant trap geometries. Comparing with Quantum Monte Carlo calculations, we quantify the onset of the fluctuation regime, where correlations beyond mean-field become important. Although the density profile depends on the microscopic parameters of the system, we show that the correlation density (the difference between the exact and the mean-field density) is accurately described by a universal expression, obtained from classical-field calculations of the homogeneous strictly two-dimensional gas. Deviations from universality, due to the finite value of the interaction or to the trap geometry, are shown to be small for current experiments. We further study coherence and pair correlations on a microscopic scale. Finite-size effects in the off-diagonal density matrix allows us to characterize the cross-over from Kosterlitz-Thouless to Bose-Einstein behavior for small particle numbers. Bose-Einstein condensation occurs below a characteristic number of particles which rapidly diverges with vanishing interactions.

cond-mat.quant-gas↗

arXiv2008

Renormalization factor and effective mass of the two-dimensional electron gas

We calculate the momentum distribution of the Fermi liquid phase of the homogeneous, two-dimensional electron gas. We show that, close to the Fermi surface, the momentum distribution of a finite system with $N$ electrons approaches its thermodynamic limit slowly, with leading order corrections scaling as $N^{-1/4}$. These corrections dominate the extrapolation of the renormalization factor, $Z$, and the single particle effective mass, $m^*$, to the infinite system size. We show how convergence can be improved analytically. In the range $1 \le r_s \le 10$, we get a lower renormalization factor $Z$ and a higher effective mass, $m^*>m$, compared to the perturbative RPA values.

cond-mat.str-el↗