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

¹ Dipartimento di Fisica, Università di Roma Tor Vergata - Via della Ricerca Scientifica 1, I-00133 Rome, Italy, EU
² INFN, Laboratori Nazionali di Frascati - Via E. Fermi 40, 00044 Frascati, Italy, EU
³ European Theoretical Spectroscopy Facility (ETSF)

^a enrico.perfetto@roma2.infn.it

Received: 22 February 2011
Accepted: 23 May 2011

Abstract

We present a comprehensive analysis of the relaxation dynamics of a Luttinger liquid subject to a sequence of sudden interaction quenches. The critical exponent β governing the decay of the steady-state propagator is expressed as an explicit functional of the switching protocol. At long distances β 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 exists no protocol to bring the initial non-interacting system in the ground state of the Luttinger liquid, albeit thermalization occurs 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.