The $1/r^2$ Integrable system: The Universal Hamiltonian for Quantum Chaos

TL;DR

This paper discusses how the 1/r^2 model serves as a universal Hamiltonian for quantum chaos, linking random matrix theory, eigenvalue evolution, and particle fractionalization to explain universal bulk correlations.

Contribution

It demonstrates the universality of the 1/r^2 model for quantum chaotic systems and provides explicit correlation functions using Bethe's Ansatz.

Findings

The 1/r^2 model is a universal Hamiltonian for quantum chaos.

Bulk space-time correlations are robust to boundary condition changes.

Explicit density-density correlations reveal fractionalization into Bethe quasi-particles.

Abstract

We summarize recent work showing that the $1/r^2$ model of interacting particles in 1-dimension is a universal Hamiltonian for quantum chaotic systems. The problem is analyzed in terms of random matrices and of the evolution of their eigenvalues under changes of parameters. The robustness of bulk space-time correlations of a many particle system to changing boundary conditions is suggested to be at the root of the universality. The explicit density-density correlation functions of the $1/r^2$ model, now available through the above mapping at two values of the coupling constant, are interpreted in the light of Bethe's {\it Ansatz}, giving a vivid picture of the fractionalization of bare particles or holes into ``quark'' like Bethe quasi-particles and holes.