Emergence of a Renormalized $1/N$ Expansion in Quenched Critical Many-Body Systems

TL;DR

This paper demonstrates how a renormalized $1/N$ expansion emerges in quenched critical many-body quantum systems, revealing a universal parameter that governs the quantum-classical transition and extends the validity of quasiclassical approximations.

Contribution

It introduces a renormalized parameter ${ m e}^{2\lambda t}/N$ that captures nonperturbative effects in critical many-body systems, extending the applicability of $1/N$ expansions.

Findings

The renormalized parameter accurately describes local divergence rates.

Quasiclassical expansions are valid to arbitrarily high orders with this parameter.

Numerical simulations confirm the theoretical predictions.

Abstract

We consider the fate of $1/N$ expansions in unstable many-body quantum systems, as realized by a quench across criticality, and show the emergence of ${\rm e}^{2\lambda t}/N$ as a renormalized parameter ruling the quantum-classical transition and accounting nonperturbatively for the local divergence rate $\lambda$ of mean-field solutions. In terms of ${\rm e}^{2\lambda t}/N$, quasiclassical expansions of paradigmatic examples of criticality, like the self-trapping transition in an integrable Bose-Hubbard dimer and the generic instability of attractive bosonic systems toward soliton formation, are pushed to arbitrarily high orders. The agreement with numerical simulations supports the general nature of our results in the appropriately combined long-time $\lambda t\to \infty$ quasiclassical $N\to \infty$ regime, out of reach of expansions in the bare parameter $1/N$. For scrambling in many-body hyperbolic systems, our results provide formal grounds to a conjectured multiexponential form of out-of-time-ordered correlators.