Beyond perturbation theory: A time-dependent approach to inelastic scattering spectroscopies in- and away from equilibrium
We propose a non-perturbative numerical approach to calculate the spectrum of a many-body Hamiltonian with time and momentum resolution by exactly recreating a scattering event using the time-dependent 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 Mott-insulating Hubbard chain after a sudden quench with the aid of the time-dependent density matrix renormalization group (tDMRG) method. Our formalism can be applied to different forms of spectroscopies, such as neutron and Compton scattering, and electron energy-loss spectroscopy (EELS), for instance.
- Pub Date:
- August 2020
- Condensed Matter - Strongly Correlated Electrons
- 10 pages, 8 figures