Quench-induced entanglement and relaxation dynamics in Luttinger liquids

Abstract

We investigate the time evolution towards the asymptotic steady state of a one dimensional interacting system after a quantum quench. We show that at finite times the latter induces entanglement between right-and left-moving density excitations, encoded in their cross-correlators, which vanishes in the long-time limit. This behavior results in a universal time-decay ∝ t −2 of the system spectral properties, in addition to non-universal power-law contributions typical of Luttinger liquids. Importantly, we argue that the presence of quench-induced entanglement clearly emerges in transport properties, such as charge and energy currents injected in the system from a biased probe, and determines their long-time dynamics. In particular, the energy fractionalization phenomenon turns out to be a promising platform to observe the universal power-law decay ∝ t −2 induced by entanglement and represents a novel way to study the corresponding relaxation mechanism.

Universal scaling of quench-induced correlations in a one-dimensional channel at finite temperature

“…In particular, we can observe that the integrand e iωτ G pp r (t, t − τ ) contributes to A pp r (ω, t) only in two distinct regions: near τ ∼ 0, where the Green function approaches its poles -see Eqs. (20,24) -and close to the boundary of the integration domain τ ∼ t. As a consequence, in the long-time limit t ω −1 one has [45] A…”

“…To study the relaxation dynamics it is useful to derive asymptotic expressions for D α,−α (t, τ ). For the zero-temperature contribution of D (0) α,−α (t, τ ) the relevant time scale is τ and for t τ one finds via [45]…”

“…Indeed, they are characterised by an infinite number of conserved quantities which allow to promptly construct their generalised Gibbs ensemble. Moreover, the unavoidable presence of interactions give rise to several intriguing effects including charge and spin fractionalisation [16,17,18,28,31,32,33,34,35,36,37,38,39,40,41,42,43], which have been also investigated in the presence of a quantum quench [44,45]. Relaxation dynamics of Luttinger liquids have been the subject of recent theoretical activity [12,14,46,47,48,49,50,51,52,53], even at finite temperature [54,55,56].…”

Spectral properties of interacting helical channels driven by Lorentzian pulses

“…In this section we discuss the intrinsic spectral properties [97,101,[109][110][111]] of the interacting system in the presence of a periodic drive. To this end, we will focus on the variation of the spectral function, with respect to its equilibrium value (when V(t)=0).…”

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] .…”