The two-body random spin ensemble and a new type of quantum phase transition

TL;DR

This paper investigates a two-body random spin ensemble, revealing a novel quantum phase transition driven by the strength of a random external field that breaks time reversal symmetry.

Contribution

It introduces a new random matrix ensemble for spins invariant under local transformations and identifies a unique quantum phase transition in a spin chain model.

Findings

Discovered a new quantum phase transition related to external field strength.

Analyzed ensemble invariance under local transformations.

Numerical evidence of phase transition in spin chain with random fields.

Abstract

We study the properties of a two-body random matrix ensemble for distinguishable spins. We require the ensemble to be invariant under the group of local transformations and analyze a parametrization in terms of the group parameters and the remaining parameters associated with the "entangling" part of the interaction. We then specialize to a spin chain with nearest neighbour interactions and numerically find a new type of quantum phase transition related to the strength of a random external field i.e. the time reversal breaking one body interaction term.