Insights from the exact analytical solution of periodically driven transverse field Ising chain

• URL: http://arxiv.org/abs/2409.08830v1
• Date: Fri, 13 Sep 2024 13:45:52 GMT
• Title: Insights from the exact analytical solution of periodically driven transverse field Ising chain
• Authors: Pritam Das, Anirban Dutta,
• Abstract summary: We derive an exact analytical expression, at stroboscopic intervals, for the time-dependent wave function of a class of integrable quantum many-body systems. To investigate long-time dynamics, we use the wave-function to obtain an exact analytical expression for the expectation value of defect density, magnetization, residual energy, fidelity, and correlation function after the $n$th drive cycle.
• Score: 1.450261153230204
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We derive an exact analytical expression, at stroboscopic intervals, for the time-dependent wave function of a class of integrable quantum many-body systems, driven by the periodic delta-kick protocol. To investigate long-time dynamics, we use the wave-function to obtain an exact analytical expression for the expectation value of defect density, magnetization, residual energy, fidelity, and correlation function after the $n$th drive cycle. Periodically driven integrable closed quantum systems absorb energy, and the long-time universal dynamics are described by the periodic generalized Gibbs ensemble(GGE). We demonstrate that the expectation values of all observables are divided into two parts: one highly oscillatory term that depends on the drive cycle $n$, and the rest of the terms are independent of it. Typically, the $n$-independent part constitutes the saturation at large $n$ and periodic GGE. The contribution from the highly oscillatory term vanishes in large $n$.

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