arXiv subjects

R. D. Nesselrodt

Publications and source records attributed to R. D. Nesselrodt.

4 recordsLinked to original sources

arXiv2021

Exact solution of two simple non-equilibrium electron-phonon and electron-electron coupled systems: the atomic limit of the Holstein-Hubbard model and the generalized Hatsugai-Komoto model

One of the challenges in many-body physics is determining the effects of phonons on strongly correlated electrons. The difficulty arises from strong correlations at differing energy scales -- for band metals, Migdal-Eliashberg theory accurately determines electron-phonon coupling effects due to the absence of vertex corrections -- but strongly correlated electrons require a more complex description and the standard Migdal-Eliashberg approach does not necessarily apply. In this work, we solve for the atomic limit Green's function of the Holstein-Hubbard model with both time-dependent electron-electron and electron-phonon couplings. We then examine the photoemission spectra (PES) of this model in and out of equilibrium. Next we use similar methods to exactly solve an extended version of the Hatsugai-Komoto model, and examine its behavior in and out of equilibrium. These calculations lead us to propose using the first moment of the photoemission spectra to signal non-equilibrium changes in electron-electron and electron-phonon couplings.

cond-mat.str-el↗

arXiv2021

Nonequilibrium spectral moment sum rules of the Holstein-Hubbard model

We derive a general procedure for evaluating the ${\rm n}$th derivative of a time-dependent operator in the Heisenberg representation and employ this approach to calculate the zeroth to third spectral moment sum rules of the retarded electronic Green's function and self-energy for a system described by the Holstein-Hubbard model allowing for arbitrary spatial and time variation of all parameters (including spatially homogeneous electric fields and parameter quenches). For a translationally invariant (but time-dependent) Hamiltonian, we also provide sum rules in momentum space. The sum rules can be applied to various different phenomena like time-resolved angle-resolved photoemission spectroscopy and benchmarking the accuracy of numerical many-body calculations. This work also corrects some errors found in earlier work on simpler models.

cond-mat.str-el↗

arXiv2021

A pedagogical derivation of dynamical susceptibilities

Dynamical two-particle susceptibilites are important for a wide range of different experiments in condensed-matter physics and beyond. Nevertheless, most textbooks avoid describing how to derive such response functions, perhaps because they are viewed as too complex. In the literature, most derivations work with generalized susceptibilities, which are more general, but require an even higher layer of complexity. In this work, we show a more direct derivation in the context of model Hamiltonians which can be mapped directly onto an impurity model. We also present an alternative derivation for the irreducible vertex in the context of the Falicov-Kimball model.

quant-ph↗

arXiv2019

Comparison Between the f-Electron and Conduction-Electron Density of States in the Falicov-Kimball Model at Low Temperature

The spinless Falicov-Kimball model is one of the simplest models of many-body physics. While the conduction-electron density of states is temperature independent in the normal state, the f-electron density of states is strongly temperature dependent---it has an orthogonality catastrophe singularity in the metallic phase and is gapped in the insulating phase. The question we address here is whether the spectral gap is the same for both electron species as T->0. We find strong evidence to indicate that the answer is affirmative.

cond-mat.str-el↗