Chaos in the thermodynamic Bethe ansatz

TL;DR

This paper demonstrates that many 1+1 dimensional quantum field theories, analyzed via a discretized thermodynamic Bethe ansatz, exhibit chaotic behavior characterized by sensitive dependence on initial conditions.

Contribution

It provides the first analysis of chaos in the thermodynamic Bethe ansatz framework for quantum field theories, using Lyapunov exponents to quantify chaos.

Findings

Many systems show positive Lyapunov exponents indicating chaos

Chaotic behavior is linked to the structure of the discretized TBA equations

Sensitivity to initial conditions is prevalent in these models

Abstract

We investigate the discretized version of the thermodynamic Bethe ansatz equation for a variety of 1+1 dimensional quantum field theories. By computing Lyapunov exponents we establish that many systems of this type exhibit chaotic behaviour, in the sense that their orbits through fixed points are extremely sensitive with regard to the initial conditions.