Charge and pairing dynamics in the attractive Hubbard model: mode coupling and the validity of linear-response theory

TL;DR

This study investigates the validity of linear-response theory in non-equilibrium dynamics of the attractive Hubbard model, revealing its applicability depends on the symmetry relationship between the pump-induced state and the external probe.

Contribution

It provides a detailed analysis of when linear-response theory holds or fails in non-equilibrium charge and pairing dynamics within the attractive Hubbard model.

Findings

Linear-response theory is valid for small to moderate non-equilibrium states with different symmetries.

Significant deviations occur when the non-equilibrium state and external field share the same symmetry.

Mode coupling effects lead to the breakdown of linear-response assumptions in certain non-equilibrium conditions.

Abstract

Pump-probe experiments have turned out as a powerful tool in order to study the dynamics of competing orders in a large variety of materials. The corresponding analysis of the data often relies on standard linear-response theory generalized to non-equilibrium situations. Here we examine the validity of such an approach within the attractive Hubbard model for which the dynamics of pairing and charge-density wave orders is computed using the time-dependent Hartree-Fock approximation (TDHF). Our calculations reveal that the `linear-response assumption' is justified for small to moderate non-equilibrium situations (i.e., pump pulses) when the symmetry of the pump-induced state differs from that of the external field. This is the case, when we consider the pairing response in a charge-ordered state or the charge-order response in a superconducting state. The situation is very different when the non-equilibrium state and the external probe field have the same symmetry. In this case, we observe significant changes of the response in magnitude but also due to mode coupling when moving away from an equilibrium state, indicating the failure of the linear-response assumption.