arXiv subjects

Teresa E. Reinhard

Publications and source records attributed to Teresa E. Reinhard.

4 recordsLinked to original sources

arXiv2024

First Principles Numerical Demonstration of Emergent Decoherent Histories

Within the histories formalism the decoherence functional is a formal tool to investigate the emergence of classicality in isolated quantum systems, yet an explicit evaluation of it from first principles has not been reported. We provide such an evaluation for up to five-time histories based on exact numerical diagonalization of the Schrödinger equation. We find a robust emergence of decoherence for slow and coarse observables of a generic random matrix model and extract a finite size scaling law by varying the Hilbert space dimension over four orders of magnitude. Specifically, we conjecture and observe an exponential suppression of coherent effects as a function of the particle number of the system. This suggests a solution to the preferred basis problem of the many worlds interpretation (or the set selection problem of the histories formalism) within a minimal theoretical framework -- without relying on environmentally induced decoherence, quantum Darwinism, Markov approximations, low-entropy initial states or ensemble averages.

quant-ph↗

arXiv2021

Approximations based on density-matrix embedding theory for density-functional theories

Recently a novel approach to find approximate exchange-correlation functionals in density-functional theory (DFT) was presented (U. Mordovina et. al., JCTC 15, 5209 (2019)), which relies on approximations to the interacting wave function using density-matrix embedding theory (DMET). This approximate interacting wave function is constructed by using a projection determined by an iterative procedure that makes parts of the reduced density matrix of an auxiliary system the same as the approximate interacting density matrix. If only the diagonal of both systems are connected this leads to an approximation of the interacting-to-non-interacting mapping of the Kohn-Sham approach to DFT. Yet other choices are possible and allow to connect DMET with other DFTs such as kinetic-energy DFT or reduced density-matrix functional theory. In this work we give a detailed review of the basics of the DMET procedure from a DFT perspective and show how both approaches can be used to supplement each other. We do so explicitly for the case of a one-dimensional lattice system, as this is the simplest setting where we can apply DMET and the one that was originally presented. Among others we highlight how the mappings of DFTs can be used to identify uniquely defined auxiliary systems and auxiliary projections in DMET and how to construct approximations for different DFTs using DMET inspired projections. Such alternative approximation strategies become especially important for DFTs that are based on non-linearly coupled observables such as kinetic-energy DFT, where the Kohn-Sham fields are no longer simply obtainable by functional differentiation of an energy expression, or for reduced density-matrix functional theories, where a straightforward Kohn-Sham construction is not feasible.

physics.chem-ph↗

arXiv2019

Self-Consistent Density-Functional Embedding: a Novel Approach for Density-Functional Approximations

In the present work, we introduce a Self-Consistent Density-Functional Embedding technique, which leaves the realm of standard energy-functional approaches in Density Functional Theory and targets directly the density-to-potential mapping that lies at its heart. Inspired by the Density Matrix Embedding Theory, we project the full system onto a set of small interacting fragments that can be solved accurately. Based on the rigorous relation of density and potential in Density Functional Theory, we then invert the fragment densities to local potentials. Combining these results in a continuous manner provides an update for the Kohn-Sham potential of the full system, which is then used to update the projection. The scheme proposed here converges to an accurate approximation for the density and the Kohn-Sham potential of the full system. Convergence to exact results can be achieved by increasing the fragment size. We find, however, that already for small embedded fragments accurate results are obtained. We benchmark our approach for molecular bond stretching in one and two dimensions and demonstrate that it reproduces the known steps and peaks that are present in the exact exchange-correlation potential with remarkable accuracy.

physics.comp-ph↗

arXiv2018

Density-matrix embedding theory study of the one-dimensional Hubbard-Holstein model

We present a density-matrix embedding theory (DMET) study of the one-dimensional Hubbard-Holstein model, which is paradigmatic for the interplay of electron-electron and electron-phonon interactions. Analyzing the single-particle excitation gap, we find a direct Peierls insulator to Mott insulator phase transition in the adiabatic regime of slow phonons in contrast to a rather large intervening metallic phase in the anti-adiabatic regime of fast phonons. We benchmark the DMET results for both on-site energies and excitation gaps against density-matrix renormalization group (DMRG) results and find excellent agreement of the resulting phase boundaries. We also compare the fully quantum treatment of phonons against the standard Born-Oppenheimer (BO) approximation. The BO approximation gives qualitatively similar results to DMET in the adiabatic regime, but fails entirely in the anti-adiabatic regime, where BO predicts a sharp direct transition from Mott to Peierls insulator, whereas DMET correctly shows a large intervening metallic phase. This highlights the importance of quantum fluctuations in the phononic degrees of freedom for metallicity in the one-dimensional Hubbard-Holstein model.

cond-mat.str-el↗