Escort distribution function of work done and diagonal entropies in quenched Luttinger liquids

TL;DR

This paper investigates the escort distribution of work in quenched Luttinger liquids, revealing universal behavior and crossovers in entropy measures and participation ratios that characterize the system's quantum dynamics.

Contribution

It introduces the escort distribution function for work in quenched Luttinger liquids and analyzes its universal properties and implications for quantum state overlaps and entropies.

Findings

Escort distribution crosses over from thermodynamic to small system limit with increasing order a.

Diagonal Rènyi entropies and IPR depend on the universal combination of initial and final parameters.

IPR shows a crossover from Gaussian to power law decay with interaction quench.

Abstract

We study the escort probability distribution function of work done during an interaction quantum quench of Luttinger liquids. It crosses over from the thermodynamic to the small system limit with increasing $a$, the order of the escort distribution, and depends on the universal combination $(|K_i-K_f|/(K_i+K_F))^a$ with $K_i$, $K_f$ the initial and final Luttinger liquid parameters, respectively. From its characteristic function, the diagonal R\'enyi entropies and the many body inverse participation ratio (IPR) are determined to evaluate the information content of the time evolved wavefunction in terms of the eigenstates of the final Hamiltonian. The hierarchy of overlaps is dominated by that of the ground states. The IPR exhibits a crossover from Gaussian to power law decay with increasing interaction quench parameter.