Interaction stabilized steady states in the driven O(N) model

TL;DR

This paper demonstrates that in the driven O(N) model at infinite N, interactions prevent indefinite energy absorption, leading to a non-trivial, synchronized steady state that avoids heating to infinite temperature, unlike free theories.

Contribution

It provides the first example of an interacting quantum system at infinite N that resists heating and maintains a non-trivial steady state under periodic driving.

Findings

Interactions prevent infinite heating in the driven O(N) model.

The steady state exhibits non-trivial correlations and synchronization.

The model remains stable at all drive frequencies, avoiding infinite temperature.

Abstract

We study periodically driven bosonic scalar field theories in the infinite N limit. It is well-known that the free theory can undergo parametric resonance under monochromatic modulation of the mass term and thereby absorb energy indefinitely. Interactions in the infinite N limit terminate this increase for any choice of the UV cutoff and driving frequency. The steady state has non-trivial correlations and is synchronized with the drive. The O(N) model at infinite N provides the first example of a clean interacting quantum system that does not heat to infinite temperature at any drive frequency.