Beyond perturbation theory: A timedependent approach to inelastic scattering spectroscopies in and away from equilibrium
Abstract
We propose a nonperturbative numerical approach to calculate the spectrum of a manybody Hamiltonian with time and momentum resolution by exactly recreating a scattering event using the timedependent Schrödinger equation. Akin an actual inelastic scattering experiment, we explicitly account for the incident and scattered particles ( e.g. photons, neutrons, electrons...) in the Hamiltonian and obtain the spectrum by measuring the energy and momentum lost by the particle after interacting with the sample. We illustrate the method by calculating the spin excitations of a Mottinsulating Hubbard chain after a sudden quench with the aid of the timedependent density matrix renormalization group (tDMRG) method. Our formalism can be applied to different forms of spectroscopies, such as neutron and Compton scattering, and electron energyloss spectroscopy (EELS), for instance.
 Publication:

arXiv eprints
 Pub Date:
 August 2020
 DOI:
 10.48550/arXiv.2008.09709
 arXiv:
 arXiv:2008.09709
 Bibcode:
 2020arXiv200809709Z
 Keywords:

 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 10 pages, 8 figures