On the thermalization of a Luttinger liquid after a sequence of sudden interaction quenches

TL;DR

This paper analyzes how a Luttinger liquid relaxes after multiple sudden interaction changes, revealing how the decay behavior depends on initial conditions, history, and protocol complexity, with implications for thermalization and adiabatic processes.

Contribution

It provides an explicit functional form for the critical exponent governing decay, explores protocol-dependent effects, and investigates the limits of adiabatic switching in Luttinger liquids.

Findings

Decay exponent depends on initial state at long distances

Memory effects are negligible at short distances

No finite-duration protocol can fully adiabatically prepare the ground state

Abstract

We present a comprehensive analysis of the relaxation dynamics of a Luttinger liquid subject to a sequence of sudden interaction quenches. We express the critical exponent $\beta$ governing the decay of the steady-state propagator as an explicit functional of the switching protocol. At long distances $\beta$ depends only on the initial state while at short distances it is also history dependent. Continuous protocols of arbitrary complexity can be realized with infinitely long sequences. For quenches of finite duration we prove that there exist no protocol to bring the initial non-interacting system in the ground state of the Luttinger liquid. Nevertheless memory effects are washed out at short-distances. The adiabatic theorem is then investigated with ramp-switchings of increasing duration, and several analytic results for both the propagator and the excitation energy are derived.