Signatures of Chaos in Non-integrable Models of Quantum Field Theory

TL;DR

This paper investigates quantum chaos signatures in non-integrable 1+1D quantum field theories using Hamiltonian truncation, revealing that level spacing statistics align with Random Matrix Theory while eigenvector distributions do not become Gaussian, even at strong perturbations.

Contribution

It demonstrates that in non-integrable QFT models, level spacings exhibit chaotic behavior consistent with RMT, but eigenvector components do not follow Gaussian distributions, challenging typical quantum chaos expectations.

Findings

Level spacing statistics follow GOE predictions.

Eigenvector component distributions differ from Gaussian.

Chaotic level statistics appear in the perturbative regime.

Abstract

We study signatures of quantum chaos in (1+1)D Quantum Field Theory (QFT) models. Our analysis is based on the method of Hamiltonian truncation, a numerical approach for the construction of low-energy spectra and eigenstates of QFTs that can be considered as perturbations of exactly solvable models. We focus on the double sine-Gordon, also studying the massive sine-Gordon and ${\phi^4}$ model, all of which are non-integrable and can be studied by this method with sufficiently high precision from small to intermediate perturbation strength. We analyze the statistics of level spacings and of eigenvector components, both of which are expected to follow Random Matrix Theory predictions. While level spacing statistics are close to the Gaussian Orthogonal Ensemble as expected, on the contrary, the eigenvector components follow a distribution markedly different from the expected Gaussian. Unlike in the typical quantum chaos scenario, the transition of level spacing statistics to chaotic behaviour takes place already in the perturbative regime. On the other hand, the distribution of eigenvector components does not appear to change or approach Gaussian behaviour, even for relatively large perturbations. Moreover, our results suggest that these features are independent of the choice of model and basis.