Energy Level Distribution of Perturbed Conformal Field Theories

TL;DR

This paper investigates the energy level spacing in perturbed conformal minimal models, revealing Poissonian statistics for integrable cases and GOE-like for non-integrable ones, with crossovers controllable by system size.

Contribution

It introduces a renormalization group improved truncated conformal spectrum approach to accurately compute spectra of large systems with over 40,000 states.

Findings

Poissonian level statistics in integrable models

GOE-like statistics in non-integrable models

Crossovers between statistical distributions controlled by system size

Abstract

We study the energy level spacing of perturbed conformal minimal models in finite volume, considering perturbations of such models that are massive but not necessarily integrable. We compute their spectrum using a renormalization group improved truncated conformal spectrum approach. With this method we are able to study systems where more than 40000 states are kept and where we determine the energies of the lowest several thousand eigenstates with high accuracy. We find, as expected, that the level spacing statistics of integrable perturbed minimal models are Poissonian while the statistics of non-integrable perturbations are GOE-like. However by varying the system size (and so controlling the positioning of the theory between its IR and UV limits) one can induce crossovers between the two statistical distributions.