Thermalization and chaos in a 1+1d QFT

• Published in: The journal of high energy physics Vol. 2023; no. 2; pp. 45 - 31
• Main Authors: Delacrétaz, Luca V., Fitzpatrick, A. Liam, Katz, Emanuel, Walters, Matthew T.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 03-02-2023; Springer Nature B.V; SpringerOpen
• Subjects: Classical and Quantum Gravitation; Coupling; Eigenvectors; Elementary Particles; Energy; Equations of state; Equilibrium; Field theory; Field Theory Hydrodynamics; Form factors; High energy physics; High temperature; Hypotheses; Matrix theory; Non-Equilibrium Field Theory; Numerical analysis; Numerical methods; Operators (mathematics); Physics; Physics and Astronomy; Quantum Dissipative Systems; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Statistics; String Theory; Theoretical physics; Thermal Field Theory; Thermalization (energy absorption); Quantum Dissipative Systems; Field Theory Hydrodynamics; Non-Equilibrium Field Theory; Thermal Field Theory
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP02(2023)045

A
bstract
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.