arXiv subjects

Joshua S. Kretchmer

Publications and source records attributed to Joshua S. Kretchmer.

5 recordsLinked to original sources

arXiv2023

A multi-fragment real-time extension of projected density matrix embedding theory: Non-equilibrium electron dynamics in extended systems

In this work, we derive a multi-fragment real-time extension of projected density matrix embedding theory (pDMET) designed to treat non-equilibrium electron dynamics in strongly correlated systems. As in the previously developed static pDMET, real-time pDMET partitions the total system into many fragments; the coupling between each fragment and the rest of the system is treated through a compact representation of the environment in terms of a quantum bath. Real-time pDMET involves simultaneously propagating the wavefunctions for each separate fragment-bath embedding system along with an auxiliary mean-field wavefunction of the total system. The equations of motion are derived by (i) projecting the time-dependent Schrodinger equation in the fragment and bath space associated with each separate fragment and by (ii) enforcing the pDMET matching conditions between the global 1-particle reduced density matrix (1-RDM) obtained from the fragment calculations and the mean-field 1-RDM at all points in time. The accuracy of the method is benchmarked through comparisons to the time-dependent density-matrix renormalization group (TD-DMRG) and time-dependent Hartree-Fock (TDHF) theory; the methods were applied to a single-impurity Anderson model and multi-impurity Anderson models with ordered and disordered distributions of the impurities. The results demonstrate a large improvement over TDHF and rapid convergence to the exact dynamics with an increase in fragment size. Our results demonstrate that real-time pDMET is a promising and flexible method to simulate non-equilibrium electron dynamics in heterogeneous systems of large size.

cond-mat.str-el↗

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↗

arXiv2018

The fate of atomic spin in atomic scattering off surfaces

We explore model electron dynamics of an atom scattering off a surface within the time-dependent complete active space self consistent field (TD-CASSCF) approximation. We focus especially on the scattering of a hydrogen atom and its resulting spin-dynamics starting from an initially spin-polarized state. Our results reveal competing electronic time-scales that are governed by the electronic structure of the surface as well as the character of the atom. The timescales and nonadiabaticity of the dynamics are reported on by the final spin-polarization of the scattered atom, which may be probed in future experiments.

cond-mat.str-el↗

arXiv2017

A real-time extension of density matrix embedding theory for non-equilibrium electron dynamics

We introduce real-time density matrix embedding theory (DMET), a dynamical quantum embedding theory for computing non-equilibrium electron dynamics in strongly correlated systems. As in the previously developed static DMET, real-time DMET partitions the system into an impurity corresponding to the region of interest coupled to the surrounding environment, which is efficiently represented by a quantum bath of the same size as the impurity. In this work, we focus on a single-impurity time-dependent theory as a first step towards a full multi-impurity theory. The equations of motion of the coupled impurity and bath embedding problem in real-time DMET are then derived using the time-dependent variational principle. The accuracy of real-time DMET is compared to that of time-dependent complete active space self-consistent field (TD-CASSCF) theory and time-dependent Hartree-Fock (TDHF) theory for a variety of quantum quenches in the single impurity Anderson model (SIAM), in which the Hamiltonian is suddenly changed (quenched) to induce a non-equilibrium state. Real-time DMET shows a marked improvement over the meanfield TDHF, converging to the exact answer even in the non-trivial Kondo regime of the SIAM. However, as in static DMET, the increased dynamic flexibility of TD-CASSCF in comparison to real-time DMET using a single impurity leads to faster convergence with respect to active space size. Our results demonstrate that real-time DMET is an efficient method well suited for the simulation of non-equilibrium electron dynamics in which strong electron correlation plays an important role.

physics.chem-ph↗

arXiv2016

Cluster size convergence of the density matrix embedding theory and its dynamical cluster formulation: a study with an auxiliary-field quantum Monte Carlo solver

We investigate the cluster size convergence of the energy and observables using two forms of density matrix embedding theory (DMET): the original cluster form (CDMET) and a new formulation motivated by the dynamical cluster approximation (DCA-DMET). Both methods are applied to the half-filled one- and two-dimensional Hubbard models using a sign-problem free auxiliary-field quantum Monte Carlo (AFQMC) impurity solver, which allows for the treatment of large impurity clusters of up to 100 sites. While CDMET is more accurate at smaller impurity cluster sizes, DCA- DMET exhibits faster asymptotic convergence towards the thermodynamic limit (TDL). We use our two formulations to produce new accurate estimates for the energy and local moment of the two-dimensional Hubbard model for U/t = 2, 4, 6. These results compare favourably with the best data available in literature, and help resolve earlier uncertainties in the moment for U/t = 2.

cond-mat.str-el↗