Structure Revealed in Randomly Interacting Boson Ground States

Bosons play an important role in the study of emergent phenomena, such as the appearance of effective degrees of freedom, symmetries, and phase transitions. In this work, we use an ensemble of Hamiltonians with two-body interactions with matrix elements randomly chosen from a normal distribution, to explore the behavior of the ground states of systems of identical bosons of spin $\ell$. We especially focus on the predominance of spin 0 (or a single boson spin $\ell$) ground states for an even (or odd) number of bosons. We find that the structure of bosonic ground state wavefunctions are not random, instead preferring to be arranged into condensates of clusters.