Solving symmetric disordered systems (by Tobias J. Osborne)

In this post I want to describe a solution to a special class of symmetric disordered quantum systems. This solution is probably not new (it is pretty hard to come up with any solvable system which hasn’t been discovered before!) but I haven’t been able to find anything quite like it in a preliminary search of the literature. So I thought I’d write it up here; if anyone has seen something like this before then please let me know! This research is intended to be part of a larger project focussed on the computational complexity of disordered quantum systems: I’m starting by collecting results on solvable models to subsequently utilise in the analysis of algorithms like the density matrix renormalisation group.