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Abstract <p>The dynamics of the one-dimensional spin model (<i>s</i> = 1/2) XXZ in the quantum “quenching” mode is investigated on a classical computer using the Qiskit and LindbladMPO software. The quantitative description of the time behavior of local magnetizations and spin correlation functions are proposed to be considered as a standard for comparative analysis with similar results previously obtained on existing noisy intermedium-scale quantum (NISQ) computers. Quantum quenching of the spin system is created at the initial time, <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11497_2025_10097_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="38" /> </InlineMediaObject> <EquationSource Format="TEX">\(t = 0\)</EquationSource> <!--PhysPNLt2570012Syurakshina-m1--> </InlineEquation>, by an abrupt (nonadiabatic) change of the spin Hamiltonian parameter. The subsequent (<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11497_2025_10097_Article_IEq2.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="38" /> </InlineMediaObject> <EquationSource Format="TEX">\(t &gt; 0\)</EquationSource> <!--PhysPNLt2570012Syurakshina-m2--> </InlineEquation>) time evolution of the reduced density matrix <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11497_2025_10097_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="30" /> </InlineMediaObject> <EquationSource Format="TEX">\(\rho (t)\)</EquationSource> <!--PhysPNLt2570012Syurakshina-m3--> </InlineEquation> of the system is traced from the solutions of the quantum Liouville equation in the case of an isolated system and its generalization in the form of the Lindblad equation for an open system interacting with the environment. In the case of an open quantum system, dissipation processes are caused by the influence of fluctuating environmental fields on the spin system.</p>

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Nonequilibrium Quantum Dynamics of a Low-Dimensional Spin System

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • L. A. Siurakshina,
  • V. Yu. Yushankhai

摘要

Abstract

The dynamics of the one-dimensional spin model (s = 1/2) XXZ in the quantum “quenching” mode is investigated on a classical computer using the Qiskit and LindbladMPO software. The quantitative description of the time behavior of local magnetizations and spin correlation functions are proposed to be considered as a standard for comparative analysis with similar results previously obtained on existing noisy intermedium-scale quantum (NISQ) computers. Quantum quenching of the spin system is created at the initial time, \(t = 0\) , by an abrupt (nonadiabatic) change of the spin Hamiltonian parameter. The subsequent ( \(t > 0\) ) time evolution of the reduced density matrix \(\rho (t)\) of the system is traced from the solutions of the quantum Liouville equation in the case of an isolated system and its generalization in the form of the Lindblad equation for an open system interacting with the environment. In the case of an open quantum system, dissipation processes are caused by the influence of fluctuating environmental fields on the spin system.