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

• URL: http://arxiv.org/abs/2607.25661v1
• Date: Tue, 28 Jul 2026 12:47:28 GMT
• Title: Discrete power-law decay of subsystem distance after a quantum quench
• Abstract summary: We present a numerical study of subsystem distance decay following a global quantum quench in the infinite one-dimensional transverse-field Ising chain.<n>We show that the late-time decay follows a discrete power law $B_A(t) sim t-$, with the exponent $$ confined to discrete values.<n>Our results reveal a universal discrete structure governing local equilibration dynamics in integrable quantum systems.
• Score: 1.2326452468513227
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $B_A(t) \sim t^{-λ}$, 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 $m_S(\varphi)$, defined on $\varphi\in[0,π]$ 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.

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