Discrete power-law decay of subsystem distance after a quantum quench

Abstract

We present a numerical study of subsystem distance decay following a global quantum quench in the infinite one-dimensional transverse-field Ising chain, using the mathematically rigorous Bures distance $B_A(t)$ to quantify the deviation of the time-evolved reduced density matrix from its stationary generalized Gibbs ensemble state. We show that the late-time decay follows a discrete power law $B_A(t)\sim t^{-\hat{I}»}$, with the exponent $\hat{I}»$ confined to discrete values: $1$, $5/4$, $3/2$, $7/4$, $2$, $5/2$, and potentially further values. The specific exponent is jointly determined by the pre- and post-quench transverse fields, as well as by properties of the symmetric excitation-fraction function $m_S(\ddot{I}†)$, defined on $\ddot{I}†\in [0,\ddot{I}€]$ to characterize the pre-quench Hamiltonian eigenstates, including continuity, boundary values, and first-derivative boundary values, among others. The previously established $t^{-3/2}$ decay for the initial ground state of the pre-quench Hamiltonian is naturally recovered as a special case of this general classification. Our results reveal a universal discrete structure governing local equilibration dynamics in integrable quantum systems.

10 pages, 4 figures

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