General interaction quenches in a Luttinger liquid

TL;DR

This paper analytically studies the dynamics of entanglement after a general interaction quench in a Luttinger liquid, using Lie algebra techniques and numerical validation on a lattice model.

Contribution

It introduces an analytical approach to describe post-quench wavefunctions in a Luttinger liquid using $ ext{su}(1,1)$ algebra, generalizing previous entanglement results.

Findings

Analytical expressions for time-evolved wavefunctions obtained.

The relationship between entanglement eigenvalues and wavefunction overlaps established.

Numerical validation performed on an XXZ lattice model.

Abstract

We discuss a general interaction quench in a Luttinger liquid described by a paired bosonic Hamiltonian. By employing $\mathsf{su}(1,1)$ Lie algebra, the post-quench time-evolved wavefunctions are obtained analytically, from which the time evolution of the entanglement in momentum space can be investigated. We note that depending on the choice of Bogoliubov quasiparticles, the expressions of wavefunctions, which describe time-evolved paired states, can take different forms. The correspondence between the largest entanglement eigenvalue in momentum space and the wavefunction overlap in quench dynamics is discussed, which generalizes the results of D\'ora {\em et al} [2016, {\em Phys. Rev. Lett.} \textbf{117}, 010603]. A numerical demonstration on an XXZ lattice model is presented via the exact diagonalization method.