Level statistics in a Heisenberg chain with random magnetic field

Abstract

Level statistics is calculated for a Heisenberg spin chain with a random magnetic field, and shown to follow that of random-matrix theory pertaining to Gaussian orthogonal ensemble, due to nonconventional time-reversal invariance. However, when a bona fide time reversal violation term is added, such as three spin interaction, the statistics follows that pertaining to Gaussian unitary ensemble.