Signatures of Chaos in Nonintegrable Models of Quantum Field Theories

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 nonintegrable 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, which are expected to follow random matrix theory predictions. While level spacing statistics are close to the Gaussian orthogonal ensemble (GOE) 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 behavior takes place already in the perturbative regime. Moreover, the distribution of eigenvector components does not appear to change or approach Gaussian behavior, even for relatively large perturbations. Our results suggest that these features are independent of the choice of model and basis.

Automated summary

We studied signatures of quantum chaos in (1 + 1)D quantum field theory models using the Hamiltonian truncation method. The level spacing statistics approach the Gaussian orthogonal ensemble (GOE), while the eigenvector components exhibit a distribution markedly different from the expected Gaussian behavior. The transition to chaotic behavior in level spacing statistics occurs in the perturbative regime, and the distribution of eigenvector components does not appear to change or approach Gaussian behavior even for relatively large perturbations.