Large-$n$ $O(n)$ with long-range interactions: integrability and resonance dynamics

• URL: http://arxiv.org/abs/2512.14868v1
• Date: Tue, 16 Dec 2025 19:33:02 GMT
• Title: Large-$n$ $O(n)$ with long-range interactions: integrability and resonance dynamics
• Authors: Guido Giachetti, Nicolo Defenu,
• Abstract summary: We study the the large-$n$ dynamics of the long-range quantum $O(n)$ model, focusing on the strong long-range regime $d$.<n>The dynamics of the model exhibits non-trivial features on mesoscopic $tsimln N$, due to the activation of parametric resonances of the nearly degenerate quantum modes.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the the large-$n$ dynamics of the long-range quantum $O(n)$ model, focusing on the strong long-range regime $α<d$. The dynamics of the model exhibits non-trivial features on mesoscopic timescales $t\sim\ln N$, due to the activation of parametric resonances of the nearly degenerate quantum modes. By using recent results establishing the integrability of the large-$n$ limit, we derive the resonance conditions, and construct the reduced multi-mode Hamiltonian that captures the finite-size dynamics. This framework yields the resonance phase diagram and clarifies when and how deviations from mean-field behavior arise. In particular, the presence of multiple resonant modes enhances the logarithmic growth of entanglement and leads to spatially modulated correlations.

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