On the origin of order from random two-body interactions

TL;DR

This paper explores how order emerges in the low-energy spectra of many-body systems with random two-body interactions, revealing that higher angular momentum sectors are more orderly than the J=0 sector, contrary to common belief.

Contribution

It demonstrates through analytical and numerical methods that higher J sectors exhibit more order, challenging the traditional view that J=0 ground states dominate.

Findings

Higher J sectors are more orderly than J=0 sectors.

The prevalence of J=0 ground states results from combining states with different energy scales.

Order in low-lying spectra arises from the structure of interactions across sectors.

Abstract

We investigate the origin of order in the low-lying spectra of many-body systems with random two-body interactions. Contrary to the common belief our study based both on analytical as well as on numerical arguments shows that these are the higher $J$-sectors whose ground states are more orderly than the ones in the J=0-sector. A predominance of J=0 ground states turns out to be the result of putting on together states with different characteristic energy scales from different $J$-sectors.