Quantum Quench in the Transverse-Field Ising Chain

We consider the time evolution of observables in the transverse-field Ising chain after a sudden quench of the magnetic field. We provide exact analytical results for the asymptotic time and distance dependence of one- and two-point correlation functions of the order parameter. We employ two complementary approaches based on asymptotic evaluations of determinants and form-factor sums. We prove that the stationary value of the two-point correlation function is not thermal, but can be described by a generalized Gibbs ensemble (GGE). The approach to the stationary state can also be understood in terms of a GGE. We present a conjecture on how these results generalize to particular quenches in other integrable models.

Figure 1

${\rho }^{xx}(\ell ,t)$ for the quench $h_0=0.3\to h=0.5$ at fixed distance $\ell =20$ and $\ell =40$ against the prediction in (4). The overall amplitude of ${\rho }^{xx}$ has been used as the same fit parameter in both cases.