Quantum quench spectroscopy of a Luttinger liquid: Ultrarelativistic density wave dynamics due to fractionalization in an XXZ chain

TL;DR

This paper investigates the dynamics of localized excitations in a quantum quench of the XXZ chain, revealing ultrarelativistic density waves caused by fractionalization, using numerical and analytical methods to explore how initial correlations influence post-quench behavior.

Contribution

It demonstrates how fractionalization in a Luttinger liquid leads to ultrarelativistic density waves in a quenched XXZ chain, combining numerical and analytical approaches.

Findings

Fractionalization causes ultrarelativistic density waves at maximum band velocity.

Post-quench dynamics reveal initial state correlations through density propagation.

The ultrarelativistic wave production is linked to fractionalization evading Pauli-blocking.

Abstract

We compute the dynamics of localized excitations produced by a quantum quench in the spin 1/2 XXZ chain. Using numerics combining the density matrix renormalization group and exact time evolution, as well as analytical arguments, we show that fractionalization due to interactions in the pre-quench state gives rise to "ultrarelativistic" density waves that travel at the maximum band velocity. The system is initially prepared in the ground state of the chain within the gapless XY phase, which admits a Luttinger liquid (LL) description at low energies and long wavelengths. The Hamiltonian is then suddenly quenched to a band insulator, after which the chain evolves unitarily. Through the gapped dispersion of the insulator spectrum, the post-quench dynamics serve as a "velocity microscope," revealing initial state particle correlations via space time density propagation. We show that the ultrarelativistic wave production is tied to the particular way in which fractionalization evades Pauli-blocking in the zero-temperature initial LL state.