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.

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.

Schrödinger Operators with Oblique Transmission Conditions in R2.

In this paper we study the spectrum of self-adjoint Schrödinger operators in L2(R2) with a new type of transmission conditions along a smooth closed curve Σ⊆R2. Although these oblique transmission conditions are formally similar to δ'-conditions on Σ (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. Furthermore, we show that these Schrödinger operators with oblique transmission conditions arise naturally as non-relativistic limits of Dirac operators with electrostatic and Lorentz scalar δ-interactions justifying their usage as models in quantum mechanics.

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 R 2 and R 3 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 δ -Shell Potentials Supported on the Straight Line.

In this note the two dimensional Dirac operator A η with an electrostatic δ -shell interaction of strength η ∈ R supported on a straight line is studied. We observe a spectral transition in the sense that for the critical interaction strengths η = ± 2 the continuous spectrum of A η inside the spectral gap of the free Dirac operator A 0 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.

Time correlation functions for quantum systems: Validating Bayesian approaches for harmonic oscillators and beyond.

The quantum harmonic oscillator is the fundamental building block to compute thermal properties of virtually any dielectric crystal at low temperatures in terms of phonons, extended further to cases with anharmonic couplings, or even disordered solids. In general, Path Integral Monte Carlo or Path Integral Molecular Dynamics methods are powerful tools to determine stochastically thermodynamic quantities without systematic bias, not relying on perturbative schemes. Addressing transport properties, for instance calculating thermal conductivity from PIMC, however, is substantially more difficult. Although correlation functions of current operators can be determined by PIMC from analytic continuation on the imaginary time axis, Bayesian methods are usually employed for the numerical inversion back to real time response functions. This task not only strongly relies on the accuracy of the PIMC data but also introduces noticeable dependence on the model used for the inversion. Here, we address both difficulties with care. In particular, we first devise improved estimators for current correlations, which substantially reduce the variance of the PIMC data. Next, we provide a neat statistical approach to the inversion problem, blending into a fresh workflow the classical stochastic maximum entropy method together with recent notions borrowed from statistical learning theory. We test our ideas on a single harmonic oscillator and a collection of oscillators with a continuous distribution of frequencies and provide indications of the performance of our method in the case of a particle in a double well potential. This work establishes solid grounds for an unbiased, fully quantum mechanical calculation of transport properties in solids.

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). Depending on the structure, the fundamental indirect gap closes between 380 and 530 GPa for ideal crystals and 330-380 GPa for quantum crystals. Beyond this pressure the system enters into a bad metal phase where the density of states at the Fermi level increases with pressure up to ∼450-500 GPa when the direct gap closes. Our work partially supports the interpretation of recent experiments in high pressure hydrogen.

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. We show that the electronic (Bloch) crystal momentum can be restored by marginalizing the total electron-ion wave function with respect to the nuclear equilibrium distribution, and we describe an explicit procedure to establish the band structure of electronic excitations for quantum crystals within the Born-Oppenheimer approximation. Based on the Kubo-Greenwood equation, we discuss the effects of nuclear motion on optical conductivity. Our methodology applies to the low temperature regime where nuclear motion is quantized and, in general, differs from the semi-classical approximation. We apply our method to study the electronic structure of C2/c-24 crystalline hydrogen at 200 K and 250 GPa and discuss the optical absorption profile of hydrogen crystals at 200 K and carbon diamond at 297 K.

Self-Adjoint Dirac Operators on Domains in R 3.

In this paper, the spectral and scattering properties of a family of self-adjoint Dirac operators in L 2 ( Ω ; C 4 ) , where Ω âŠ‚ R 3 is either a bounded or an unbounded domain with a compact C 2 -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. The analysis of the perturbation term in this formula leads to a description of the spectrum and a Birman-Schwinger principle, a qualitative understanding of the scattering properties in the case that Ω is an exterior domain, and corresponding trace formulas.

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. Remarkably, this spatial arrangement correlates directly with the concentration of defects in the exciton density, which is strongly decreased in the quasicondensed region, consistent with a superfluid phase. Thus, our observations point towards a Berezinskii-Kosterlitz-Thouless crossover for two-dimensional excitons.

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. Recent experiments reported contrasting results about the location of the transition. Theoretical results based on density functional theory are also very scattered. We report highly accurate coupled electron-ion Monte Carlo calculations of this transition, finding results that lie between the two experimental predictions, close to that measured in diamond anvil cell experiments but at 25-30 GPa higher pressure. The transition along an isotherm is signaled by a discontinuity in the specific volume, a sudden dissociation of the molecules, a jump in electrical conductivity, and loss of electron localization.

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. For two dimensional ^{4}He, we also show that the iterative backflow wave function can describe both the liquid and the solid phase with the same functional form-a feature shared with the shadow wave function, but now joined by much higher accuracy. We also achieve significant progress for liquid ^{3}He in three dimensions, improving previous variational and fixed-node energies.

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. Starting from the Hartree-Fock method, we show that the GW and the BSE yield impressively accurate results on excitation energies and oscillator strength, systematically improving the time-dependent Hartree-Fock method. These findings suggest that the accuracy of the BSE and GW approximations is not significantly limited by self-interaction and self-screening problems even in this few electron limit. We further discuss our results in comparison to those obtained by time-dependent density-functional theory.

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. Around 50 GPa we find a maximum compression of 4.85. This compression is approximately 5.5% higher than previous theoretical predictions and 15% higher than the most accurate experimental data. Thus first-principles simulations encompassing the most advanced techniques are in disagreement with the results of the best experiments.

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. 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 a Bose bad-metal phase as a precursor of the Bose-glass phase.

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 Cz for the Dirac equation in the two- and three-dimensional situation. The map Cz is the strongly singular integral operator having the integral kernel of the resolvent of the free Dirac operator A0 and z belongs to the resolvent set of A0. In the case of smooth boundaries fine mapping properties and a decomposition of Cz in a 'positive' and 'negative' part are analyzed. The obtained results can be applied in the treatment of Dirac operators with singular electrostatic, Lorentz scalar, and anomalous magnetic interactions that are combined in a critical way.

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. 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) proportionally (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.