Nonrelativistic Limit of Generalized MIT Bag Models and Spectral Inequalities.

For a family of self-adjoint Dirac operators subject to generalized MIT bag boundary conditions on domains in , it is shown that the nonrelativistic limit in the norm resolvent sense is the Dirichlet Laplacian. This allows to transfer spectral geometry results for Dirichlet Laplacians to Dirac operators for large .

Static Self-Energy and Effective Mass of the Homogeneous Electron Gas from Quantum Monte Carlo Calculations.

We discuss the methodology of quantum Monte Carlo calculations of the effective mass based on the static self-energy Σ(k,0). We then use variational Monte Carlo calculations of Σ(k,0) of the homogeneous electron gas at various densities to obtain results very close to perturbative G_{0}W_{0} calculations for values of the density parameter 1≤r_{s}≤10. The obtained values for the effective mass are close to diagrammatic Monte Carlo results and disagree with previous quantum Monte Carlo calculations based on a heuristic mapping of excitation energies to those of an ideal gas.

On the Single Layer Boundary Integral Operator for the Dirac Equation.

This paper is devoted to the analysis of the single layer boundary integral operator for the Dirac equation in the two- and three-dimensional situation. The map is the strongly singular integral operator having the integral kernel of the resolvent of the free Dirac operator and belongs to the resolvent set of . In the case of smooth boundaries fine mapping properties and a decomposition of in a 'positive' and 'negative' part are analyzed.

Schrödinger Operators with Oblique Transmission Conditions in .

In this paper we study the spectrum of self-adjoint Schrödinger operators in with a new type of transmission conditions along a smooth closed curve . Although these transmission conditions are formally similar to -conditions on (instead of the normal derivative here the Wirtinger derivative is used) the spectral properties are significantly different: it turns out that for attractive interaction strengths the discrete spectrum is always unbounded from below. Besides this unexpected spectral effect we also identify the essential spectrum, and we prove a Krein-type resolvent formula and a Birman-Schwinger principle.

Stable Solid Molecular Hydrogen above 900 K from a Machine-Learned Potential Trained with Diffusion Quantum Monte Carlo.

We survey the phase diagram of high-pressure molecular hydrogen with path integral molecular dynamics using a machine-learned interatomic potential trained with quantum Monte Carlo forces and energies. Besides the HCP and C2/c-24 phases, we find two new stable phases both with molecular centers in the Fmmm-4 structure, separated by a molecular orientation transition with temperature. The high temperature isotropic Fmmm-4 phase has a reentrant melting line with a maximum at higher temperature (1450 K at 150 GPa) than previously estimated and crosses the liquid-liquid transition line around 1200 K and 200 GPa.

Dirac operator spectrum in tubes and layers with a zigzag-type boundary.

We derive a number of spectral results for Dirac operators in geometrically nontrivial regions in and of tube or layer shapes with a zigzag-type boundary using the corresponding properties of the Dirichlet Laplacian.

Spectral Transition for Dirac Operators with Electrostatic -Shell Potentials Supported on the Straight Line.

In this note the two dimensional Dirac operator with an electrostatic -shell interaction of strength supported on a straight line is studied. We observe a spectral transition in the sense that for the critical interaction strengths the continuous spectrum of inside the spectral gap of the free Dirac operator collapses abruptly to a single point.

Bath-Induced Zeno Localization in Driven Many-Body Quantum Systems.

We study a quantum interacting spin system subject to an external drive and coupled to a thermal bath of vibrational modes, uncorrelated for different spins, serving as a model for dynamic nuclear polarization protocols. We show that even when the many-body eigenstates of the system are ergodic, a sufficiently strong coupling to the bath may effectively localize the spins due to many-body quantum Zeno effect. Our results provide an explanation of the breakdown of the thermal mixing regime experimentally observed above 4-5 K in these protocols.

Quasicondensation of Bilayer Excitons in a Periodic Potential.

We study two-dimensional excitons confined in a lattice potential, for high fillings of the lattice sites. We show that a quasicondensate is possibly formed for small values of the lattice depth, but for larger ones the critical phase-space density for quasicondensation rapidly exceeds our experimental reach, due to an increase of the exciton effective mass. On the other hand, in the regime of a deep lattice potential where excitons are strongly localized at the lattice sites, we show that an array of phase-independent quasicondensates, different from a Mott insulator, is realized.

Electronic structure and optical properties of quantum crystals from first principles calculations in the Born-Oppenheimer approximation.

We develop a formalism to accurately account for the renormalization of the electronic structure due to quantum and thermal nuclear motions within the Born-Oppenheimer approximation. We focus on the fundamental energy gap obtained from electronic addition and removal energies from quantum Monte Carlo calculations in either the canonical or grand-canonical ensembles. The formalism applies as well to effective single electron theories such as those based on density functional theory.

Self-Adjoint Dirac Operators on Domains in .

In this paper, the spectral and scattering properties of a family of self-adjoint Dirac operators in , where is either a bounded or an unbounded domain with a compact -smooth boundary, are studied in a systematic way. These operators can be viewed as the natural relativistic counterpart of Laplacians with boundary conditions as of Robin type. Our approach is based on abstract boundary triple techniques from extension theory of symmetric operators and a thorough study of certain classes of (boundary) integral operators, that appear in a Krein-type resolvent formula.

Itinerant-Electron Magnetism: The Importance of Many-Body Correlations.

Do electrons become ferromagnetic just because of their repulsive Coulomb interaction? Our calculations on the three-dimensional electron gas imply that itinerant ferromagnetism of delocalized electrons without lattice and band structure, the most basic model considered by Stoner, is suppressed due to many-body correlations as speculated already by Wigner, and a possible ferromagnetic transition lowering the density is precluded by the formation of the Wigner crystal.

Energy Gap Closure of Crystalline Molecular Hydrogen with Pressure.

We study the gap closure with pressure of crystalline molecular hydrogen. The gaps are obtained from grand-canonical quantum Monte Carlo methods properly extended to quantum and thermal crystals, simulated by coupled electron ion Monte Carlo methods. Nuclear zero point effects cause a large reduction in the gap (∼2  eV).

Defect Proliferation at the Quasicondensate Crossover of Two-Dimensional Dipolar Excitons Trapped in Coupled GaAs Quantum Wells.

We study ultracold dipolar excitons confined in a 10  μm trap of a double GaAs quantum well. Based on the local density approximation, we unveil for the first time the equation of state of excitons. Specifically, in this regime and below a critical temperature of about 1 K, we show that for a local density n∼(2-3)×10^{10}  cm^{-2} a coherent quasicondensate phase forms in the inner region of the trap, encircled by a more dilute and normal component in the outer rim.

Nonlinear Network Description for Many-Body Quantum Systems in Continuous Space.

We show that the recently introduced iterative backflow wave function can be interpreted as a general neural network in continuum space with nonlinear functions in the hidden units. Using this wave function in variational Monte Carlo simulations of liquid ^{4}He in two and three dimensions, we typically find a tenfold increase in accuracy over currently used wave functions. Furthermore, subsequent stages of the iteration procedure define a set of increasingly good wave functions, each with its own variational energy and variance of the local energy: extrapolation to zero variance gives energies in close agreement with the exact values.

Helium Atom Excitations by the GW and Bethe-Salpeter Many-Body Formalism.

The helium atom is the simplest many-body electronic system provided by nature. The exact solution to the Schrödinger equation is known for helium ground and excited states, and it represents a benchmark for any many-body methodology. Here, we check the ab initio many-body GW approximation and the Bethe-Salpeter equation (BSE) against the exact solution for helium.

Confidence and efficiency scaling in variational quantum Monte Carlo calculations.

Based on the central limit theorem, we discuss the problem of evaluation of the statistical error of Monte Carlo calculations using a time-discretized diffusion process. We present a robust and practical method to determine the effective variance of general observables and show how to verify the equilibrium hypothesis by the Kolmogorov-Smirnov test. We then derive scaling laws of the efficiency illustrated by variational Monte Carlo calculations on the two-dimensional electron gas.

Fermion sign problem in imaginary-time projection continuum quantum Monte Carlo with local interaction.

We use the shadow wave function formalism as a convenient model to study the fermion sign problem affecting all projector quantum Monte Carlo methods in continuum space. We demonstrate that the efficiency of imaginary-time projection algorithms decays exponentially with increasing number of particles and/or imaginary-time propagation. Moreover, we derive an analytical expression that connects the localization of the system with the magnitude of the sign problem, illustrating this behavior through numerical results.

Liquid-liquid phase transition in hydrogen by coupled electron-ion Monte Carlo simulations.

The phase diagram of high-pressure hydrogen is of great interest for fundamental research, planetary physics, and energy applications. A first-order phase transition in the fluid phase between a molecular insulating fluid and a monoatomic metallic fluid has been predicted. The existence and precise location of the transition line is relevant for planetary models.

Molecular-Atomic Transition along the Deuterium Hugoniot Curve with Coupled Electron-Ion Monte Carlo Simulations.

We have performed simulations of the principal deuterium Hugoniot curve using coupled electron-ion Monte Carlo calculations. Using highly accurate quantum Monte Carlo methods for the electrons, we study the region of maximum compression along the 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.

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, by using large-scale quantum Monte Carlo simulations at finite temperature. 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.

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 theory. The nonzero 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 behavior in the quasiuniform part of the cloud near the trap center.

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 calculations for various densities and extrapolate the momentum distribution and the kinetic and potential energies to the thermodynamic limit. Our results on the renormalization factor allow us to validate approximate G0W0 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.

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 wave vector. This yields an accurate measure of the renormalization factor that we compare with quantum Monte Carlo and G0W0 calculations performed both on crystalline sodium and on the homogeneous electron gas.