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<p>We study SU(<i>N</i>) spin systems that mimic the behavior of particles in <i>N</i>-dimensional de Sitter space for <i>N</i> = 2, 3. Their Hamiltonians describe a dynamical system with hyperbolic fixed points, leading to emergent quasinormal modes at the quantum level. These manifest as quasiparticle peaks in the density of states. For a particle in 2-dimensional de Sitter, we find both principal and complementary series densities of states from a PT-symmetric version of the Lipkin-Meshkov-Glick model, having two hyperbolic fixed points in the classical phase space. We then study different spectral and dynamical properties of this class of models, including level spacing statistics, two-point functions, squared commutators, spectral form factor, Krylov operator and state complexity. We find that, even though the early-time properties of these quantities are governed by the saddle points — thereby in some cases mimicking corresponding properties of chaotic systems, a close look at the late-time behavior reveals the integrable nature of the system.</p>

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Quasinormal modes and complexity in saddle-dominated SU(N) spin systems

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月3日

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  • Sergio E. Aguilar-Gutierrez,
  • Yichao Fu,
  • Kuntal Pal,
  • Klaas Parmentier

摘要

We study SU(N) spin systems that mimic the behavior of particles in N-dimensional de Sitter space for N = 2, 3. Their Hamiltonians describe a dynamical system with hyperbolic fixed points, leading to emergent quasinormal modes at the quantum level. These manifest as quasiparticle peaks in the density of states. For a particle in 2-dimensional de Sitter, we find both principal and complementary series densities of states from a PT-symmetric version of the Lipkin-Meshkov-Glick model, having two hyperbolic fixed points in the classical phase space. We then study different spectral and dynamical properties of this class of models, including level spacing statistics, two-point functions, squared commutators, spectral form factor, Krylov operator and state complexity. We find that, even though the early-time properties of these quantities are governed by the saddle points — thereby in some cases mimicking corresponding properties of chaotic systems, a close look at the late-time behavior reveals the integrable nature of the system.