Spread complexity evolution in quenched interacting quantum systems

TL;DR

This paper studies the evolution of spread complexity in quantum many-body systems after a sudden quench, revealing universal early quadratic growth and system-dependent late-time behavior in integrable and chaotic models.

Contribution

It provides a detailed analysis of spread complexity dynamics in quenched quantum systems, highlighting universal and system-specific growth patterns across different models.

Findings

Universal quadratic growth of spread complexity shortly after quench

Different late-time behaviors depending on system type and survival probability

Linear growth and saturation of complexity in chaotic models

Abstract

We analyse time evolution of spread complexity (SC) in an isolated interacting quantum many-body system when it is subjected to a sudden quench. The differences in characteristics of the time evolution of the SC for different time scales is analysed, both in integrable and chaotic models. For a short time after the quench, the SC shows universal quadratic growth, irrespective of the initial state or the nature of the Hamiltonian, with the time scale of this growth being determined by the local density of states. The characteristics of the SC in the next phase depend upon the nature of the system, and we show that depending upon whether the survival probability of an initial state is Gaussian or exponential, the SC can continue to grow quadratically, or it can show linear growth. To understand the behaviour of the SC at late times, we consider sudden quenches in two models, a full random matrix in the Gaussian orthogonal ensemble, and a spin-1/2 system with disorder. We observe that for the full random matrix model and the chaotic phase of the spin-1/2 system, the complexity shows linear growth at early times and saturation at late times. The full random matrix case shows a peak in the intermediate time region, whereas this feature is less prominent in the spin-1/2 system, as we explain.