Reptation quantum Monte Carlo for lattice Hamiltonians with a directed-update scheme

We provide an extension to lattice systems of the reptation quantum Monte Carlo algorithm, originally devised for continuous Hamiltonians. For systems affected by the sign problem, a method to systematically improve upon the so-called fixed-node approximation is also proposed. The generality of the method, which also takes advantage of a canonical worm algorithm scheme to measure off-diagonal observables, makes it applicable to a vast variety of quantum systems and eases the study of their ground-state and excited-states properties. As a case study, we investigate the quantum dynamics of the one-dimensional Heisenberg model and we provide accurate estimates of the ground-state energy of the two-dimensional fermionic Hubbard model

The itinerant ferromagnetic phase of the Hubbard model

Using a newly developed quantum Monte Carlo technique, we provide strong evidence for the stability of a saturated ferromagnetic phase in the high-density regime of the two-dimensional infinite-U Hubbard model. By decreasing the electron density, a discontinuous transition to a paramagnetic phase is observed, accompanied by a divergence of the susceptibility on the paramagnetic side. This behavior, resulting from a high degeneracy among different spin sectors, is consistent with an infinite-order phase transition. The remarkable stability of itinerant ferromagnetism renews the hope to describe this phenomenon within a purely kinetic mechanism and will facilitate the validation of experimental quantum simulators with cold atoms loaded in optical lattices

Invariance principles in the theory and computation of transport coefficients

Abstract: In this work, we elaborate on two recently discovered invariance principles, according to which transport coefficients are, to a large extent, independent of the microscopic definition of the densities and currents of the conserved quantities being transported (energy, momentum, mass, charge). The first such principle, gauge invariance, allows one to define a quantum adiabatic energy current from density-functional theory, from which the heat conductivity can be uniquely defined and computed using equilibrium ab initio molecular dynamics. When combined with a novel topological definition of atomic oxidation states, gauge invariance also sheds new light onto the mechanisms of charge transport in ionic conductors. The second principle, convective invariance, allows one to extend the analysis to multi-component systems. These invariance principles can be combined with new spectral analysis methods for the current time series to be fed into the Green–Kubo formula to obtain accurate estimates of transport coefficients from relatively short molecular dynamics simulations. Graphic abstract: [Figure not available: see fulltext.

Temperature- and vacancy-concentration-dependence of heat transport in Li3ClO from multi-method numerical simulations

Despite governing heat management in any realistic device, the microscopic mechanisms of heat transport in all-solid-state electrolytes are poorly known: existing calculations, all based on simplistic semi-empirical models, are unreliable for superionic conductors and largely overestimate their thermal conductivity. In this work, we deploy a combination of state-of-the-art methods to calculate the thermal conductivity of a prototypical Li-ion conductor, the Li3ClO antiperovskite. By leveraging ab initio, machine learning, and force-field descriptions of interatomic forces, we are able to reveal the massive role of anharmonic interactions and diffusive defects on the thermal conductivity and its temperature dependence, and to eventually embed their effects into a simple rationale which is likely applicable to a wide class of ionic conductors

Thermal and Tidal Evolution of Uranus with a Growing Frozen Core

The origin of the very low luminosity of Uranus is unknown, as is the source of the internal tidal dissipation required by the orbits of the Uranian moons. Models of the interior of Uranus often assume that it is inviscid throughout, but recent experiments show that this assumption may not be justified; most of the interior of Uranus lies below the freezing temperature of H2O. We find that the stable solid phase of H2O, which is superionic, has a large viscosity controlled by the crystalline oxygen sublattice. We examine the consequences of finite viscosity by combining ab initio determinations of the thermal conductivity and other material properties of superionic H2O with a thermal evolution model that accounts for heat trapped in the growing frozen core. The high viscosity provides a means of trapping heat in the deep interior while also providing a source of tidal dissipation. The frozen core grows with time because its outer boundary is governed by the freezing transition rather than compositional layering. We find that the presence of a growing frozen core explains the anomalously low heat flow of Uranus. Our thermal evolution model also predicts time-varying tidal dissipation that matches the requirements of the orbits of Miranda, Ariel, and Umbriel. We make predictions that are testable by future space missions, including the tidal Love number of Uranus and the current recessional rates of its moons

Topology, Oxidation States, and Charge Transport in Ionic Conductors

Recent theoretical advances, based on a combination of concepts from Thouless' topological theory of adiabatic charge transport and a newly introduced gauge-invariance principle for transport coefficients, have permitted to connect (and reconcile) Faraday's picture of ionic transport—whereby each atom carries a well-defined integer charge—with a rigorous quantum description of the electronic charge-density distribution, which hardly suggests its partition into well defined atomic contributions. In this paper, these progresses are reviewed; in particular, it is shown how, by relaxing some general topological conditions, charge may be transported in ionic conductors without any net ionic displacements. After reporting numerical experiments which corroborate these findings, a new connection between the topological picture and the well-known Marcus–Hush theory of electron transfer is introduced in terms of the topology of adiabatic paths drawn by atomic trajectories. As a significant byproduct, the results reviewed here permit to classify different regimes of ionic transport according to the topological properties of the electronic structure of the conducting material. Finally, a few recent applications to energy materials and planetary sciences are reported

Self-interaction and transport of solvated electrons in molten salts

The dynamics of (few) electrons dissolved in an ionic fluid-as when a small amount of metal is added to a solution while upholding its electronic insulation-manifests interesting properties that can be ascribed to nontrivial topological features of particle transport (e.g., Thouless' pumps). In the adiabatic regime, the charge distribution and the dynamics of these dissolved electrons are uniquely determined by the nuclear configuration. Yet, their localization into effective potential wells and their diffusivity are dictated by how the self-interaction is modeled. In this article, we investigate the role of self-interaction in the description of the localization and transport properties of dissolved electrons in non-stoichiometric molten salts. Although the account for the exact (Fock) exchange strongly localizes the dissolved electrons, decreasing their tunneling probability and diffusivity, we show that the dynamics of the ions and of the dissolved electrons are largely uncorrelated, irrespective of the degree to which the electron self-interaction is treated and in accordance with topological arguments