Thermalization and chaos in a 1+1d QFT

TL;DR

This paper investigates chaos and thermodynamics in a 1+1d scalar quantum field theory at strong coupling using numerical methods, revealing RMT statistics, eigenstate thermalization, and spectral form factor behavior consistent with chaotic quantum systems.

Contribution

It introduces a numerical approach to study chaos and thermodynamics in a 1+1d QFT, demonstrating RMT statistics, eigenstate thermalization, and a new technique for spectral form factor analysis.

Findings

Eigenstate spectrum follows Wigner-Dyson statistics.

Eigenstates exhibit RMT statistics with some scar states at weak coupling.

Results align with Conformal Field Theory expectations at high temperatures.

Abstract

We study aspects of chaos and thermodynamics at strong coupling in a scalar model using LCT numerical methods. We find that our eigenstate spectrum satisfies Wigner-Dyson statistics and that the coefficients describing eigenstates in our basis satisfy Random Matrix Theory (RMT) statistics. At weak coupling, though the bulk of states satisfy RMT statistics, we find several scar states as well. We then use these chaotic states to compute the equation of state of the model, obtaining results consistent with Conformal Field Theory (CFT) expectations at temperatures above the scale of relevant interactions. We also test the Eigenstate Thermalization Hypothesis by computing the expectation value of local operators in eigenstates, and check that their behavior is consistent with thermal CFT values at high temperatures. Finally, we compute the Spectral Form Factor (SFF), which has the expected behavior associated with the equation of state at short times and chaos at long times. We also propose a new technique for extracting the connected part of the SFF without the need of disorder averaging by using different symmetry sectors.