2026/07/28 by Bin Sui, Jiaju Zhang
#quant-ph #cond-mat.stat-mech #cond-mat.str-el #hep-th
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 BA(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 BA(t) ∼ t-λ, with the exponent λ 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 mS(φ), defined on φ∈[0,π] 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.