Analytic results for a quantum quench from free to hard-core one-dimensional bosons

Abstract

It is widely believed that the stationary properties after a quantum quench in integrable systems can be described by a generalized Gibbs ensemble (GGE), even if all of the analytical evidence is based on free theories in which the pre-and postquench modes are linearly related. In contrast, we consider the experimentally relevant quench of the one-dimensional Bose gas from zero to infinite interaction, in which the relation between modes is nonlinear, and consequently Wick's theorem does not hold. We provide exact analytical results for the time evolution of the dynamical density-density correlation function at any time after the quench and we prove that its stationary value is described by a GGE in which Wick's theorem is restored.

Solution for an interaction quench in the Lieb-Liniger Bose gas

“…This easily reproduces the recently calculated result of Ref. [32] and therefore represents a nontrivial check of the validity of expression (16) for any time t after the quench.…”

Relaxation dynamics of the Lieb-Liniger gas following an interaction quench: A coordinate Bethe-ansatz analysis

“…Results for the relaxation dynamics of the LL model following an interaction-strength quench have previously been obtained in the limiting cases of quenches to the noninteracting limit [55,56] and to the opposite TonksGirardeau (TG) limit of infinitely strong interactions [57][58][59][60], where the dynamics are governed by free-particle propagation. For quenches to finite interaction strengths, the relaxation dynamics have been investigated using a range of techniques, including exact diagonalization within a truncated momentum-mode basis [61], quasiexact numerical simulations of lattice discretizations of the model [62,63], and nonperturbative approximations arXiv:1407.4998v3 [cond-mat.quant-gas] 14 Feb 2015 derived using functional-integral techniques [35][36][37][38]64].…”

“…In particular, we calculate the time evolution of the momentum distribution of the Bose gas, which is not easily accessible within other Bethe-ansatz-based approaches [58], and find results qualitatively consistent with the results of functional-integral calculations of the relaxation dynamics [35][36][37][38]64]. Our results for the second-order coherence function reveal the propagation of correlation waves, as previously observed in simulations of quenches within lattice discretizations of the LL model [62,63] and quenches to the TG limit [57,58]. Our numerical approach in terms of the N -particle energy eigenstates of the LL Hamiltonian also allows us to calculate the quantum fidelity between the time-evolved state of the system following the quench and the initial state, which decays over time as the eigenstate dephasing that underlies the relaxation dynamics [68] takes place.…”

Non-equilibrium dynamics of isolated quantum systems

“…[52]) the explicit evaluation of the long time limit of many observables [63] whose values agree with the previously constructed GGE. It is worth mentioning that the quench from c = 0 to c = ∞ has been treated with more elementary techniques [46], whose results are reproduced by the proper limit of the general construction [63]. The anisotropic Heisenberg spin chain has a similar story, but with a different end.…”

“…Other examples includes quenches in lattice field theories [18,[26][27][28][29], Luttinger model quartic term quench [30][31][32], transverse field quench in Ising chain [16,25,[33][34][35][36][37][38][39][40][41][42][43], quenches to a gas of hard-core bosons [44][45][46], and many more. In all these examples it has been shown that indeed the GGE holds.…”