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

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Giachetti, Guido, Defenu, Nicolo
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866915680748568576
author Giachetti, Guido
Defenu, Nicolo
author_facet Giachetti, Guido
Defenu, Nicolo
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2512_14868
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Large-$n$ $O(n)$ with long-range interactions: integrability and resonance dynamics
Giachetti, Guido
Defenu, Nicolo
Statistical Mechanics
Quantum Physics
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.
title Large-$n$ $O(n)$ with long-range interactions: integrability and resonance dynamics
topic Statistical Mechanics
Quantum Physics
url https://arxiv.org/abs/2512.14868