Long-time divergences in the nonlinear response of gapped one-dimensional many-particle systems

TL;DR

This paper investigates long-time divergences in the nonlinear response of one-dimensional gapped many-particle systems, revealing linear divergences in four-point functions and their semiclassical explanation, with implications for experiments.

Contribution

It demonstrates that certain four-point functions diverge linearly over time in gapped 1D systems and provides a semiclassical framework to understand this behavior, verified in the transverse field Ising model.

Findings

Four-point functions diverge linearly in time differences.

Semiclassical wave packet analysis accurately predicts long-time behavior.

Subleading corrections grow as the square root of time differences.

Abstract

We consider one dimensional many-particle systems that exhibit kinematically protected single-particle excitations over their ground states. We show that momentum and time-resolved 4-point functions of operators that create such excitations diverge linearly in particular time differences. This behaviour can be understood by means of a simple semiclassical analysis based on the kinematics and scattering of wave packets of quasiparticles. We verify that our wave packet analysis correctly predicts the long-time limit of the four-point function in the transverse field Ising model through a form factor expansion. We present evidence in favour of the same behaviour in integrable quantum field theories. In addition, we extend our discussion to experimental protocols where two times of the four-point function coincide, e.g. 2D coherent spectroscopy and pump-probe experiments. Finally, focusing on the Ising model, we discuss subleading corrections that grow as the square root of time differences. We show that the subleading corrections can be correctly accounted for by the same semiclassical analysis, but also taking into account wave packet spreading.