Quantum quenches in the Luttinger model and its close relatives

Abstract

A number of results on quantum quenches in the Luttinger and related models are surveyed with emphasis on post-quench correlations. For the Luttinger model and initial gaussian states, we discuss both sudden and smooth quenches of the interaction and the emergence of a steady state described by a generalized Gibbs ensemble. Comparisons between analytics and numerics, and the question of universality or lack thereof are also discussed. The relevance of the theoretical results to current and future experiments in the fields of ultracold atomic gases and mesoscopic systems of electrons is also briefly touched upon. Wherever possible, our approach is pedagogical and self-contained. This work is dedicated to the memory of our colleague Alejandro Muramatsu.

Remotely detecting the signal of a local decohering process in spin chains

“…As the distance between the sites increase the interaction strength decreases by power law given in Eq (12). The slope function (dF/dt)| t 0 is plotted against the site index in Fig 2(d), exhibits this same trend.…”

Quench-induced entanglement and relaxation dynamics in Luttinger liquids

“…At t = 0, the system is brought out-of-equilibrium by suddenly changing the strength of inter-particle interactions. The subsequent dynamics is thus governed by the final Hamiltonian H f [22,23]. In particular, the two Hamiltonians involved in the quench can be written as (hereafter = 1) [30][31][32] …”

“…An intriguing possibility to drive a quantum system out of equilibrium is to perform a quantum quench, i.e. a sudden change in time of some of its parameters [21][22][23]. Such a procedure is available in state-of-the-art systems of cold atoms [11], in which transport and real-time control experiments have been recently reported [13][14][15][24][25][26].…”

Nonmonotonic response and light-cone freezing in fermionic systems under quantum quenches from gapless to gapped or partially gapped states

“…Quantum quenches have been studied in a wide range of systems with the property that a change in a parameter of the Hamiltonian deeply affects the physical properties of the system itself. Interaction quenches in Luttinger liquids [24][25][26][27][28][29][30][31][32][33][34][35][36] and magnetic field quenches in the one-dimensional (1D) Ising model [37][38][39][40][41][42][43][44][45][46][47] are prominent examples in this direction. Furthermore, at the level of free fermions, quantum quenches between gapped phases characterized by different Chern numbers have also been studied [48][49][50][51] .…”

“…2 for the SOC wire model, in the case of (a) small quench ∆ (2) = 0.3 and (b) large quench ∆ (2) = 2. For a small quench, G (2) (x, t) exhibits a typical lightcone behavior 17,24,25 and information of the quench is therefore able to propagate throughout the system. This leaves a finite "trail" in x = 0, which eventually results in a finite value of M (2) at large times.…”