Beyond perturbation theory: A time-dependent approach to inelastic scattering spectroscopies in- and away from equilibrium

TL;DR

This paper introduces a non-perturbative, time-dependent numerical method for calculating inelastic scattering spectra in many-body systems, explicitly modeling incident and scattered particles to improve accuracy.

Contribution

The authors develop a novel time-dependent approach that explicitly includes incident and scattered particles, enabling accurate inelastic scattering spectra calculations beyond perturbation theory.

Findings

Successfully calculated spin excitations in a Hubbard chain after a quench.

Method applicable to various spectroscopies like neutron, Compton, and EELS.

Demonstrated the approach with tDMRG for a Mott insulator.

Abstract

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 Schr\"odinger 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.