Bipartite Sachdev-Ye models with Read-Saleur symmetries

We introduce an <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>SU</a:mi><a:mo>(</a:mo><a:mi>M</a:mi><a:mo>)</a:mo></a:mrow></a:math>-symmetric disordered bipartite spin model with unusual characteristics. Although superficially similar to the Sachdev-Ye (SY) model, it has several markedly different properties for <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mi>M</b:mi><b:mo>≥</b:mo><b:mn>3</b:mn></b:mrow></b:math>. In particular, it has a large nontrivial nullspace whose dimension grows exponentially with system size. The states in this nullspace are frustration-free and are ground states when the interactions are ferromagnetic. The exponential growth of the nullspace leads to Hilbert-space fragmentation and a violation of the eigenstate thermalization hypothesis. We demonstrate that the commutant algebra responsible for this fragmentation is a nontrivial subalgebra of the Read-Saleur commutant algebra of certain nearest-neighbor models such as the spin-1 biquadratic spin chain. We also discuss the low-energy behavior of correlations for the disordered version of this model in the limit of a large number of spins and large <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mi>M</c:mi></c:math>, using techniques similar to those applied to the SY model. We conclude by generalizing the Shiraishi-Mori embedding formalism to nonlocal models, and apply it to turn some of our nullspace states into quantum many-body scars.