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arXiv · 2506.05458

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

Sergio E. Aguilar-Gutierrez·Yichao Fu·Kuntal Pal·Klaas Parmentier
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Abstract

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.

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Sergio E. Aguilar-Gutierrez, Yichao Fu, Kuntal Pal, Klaas Parmentier. 2025-06-05. Quasinormal modes and complexity in saddle-dominated SU(N) spin systems. https://arxiv.org/abs/2506.05458

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