Study of entanglement and phase transitions in the coupled top systems with standard and nonstandard symmetries
We study classical and quantum versions of a coupled top system in the absence and the presence of nonlinear torsion in the individual top. The model without the torsion and couples two identical tops is well-known in the literature as the Feingold-Peres (FP) model. The permutation and chiral symmetries are preserved in the FP model. This model is classified under the BDI or chiral orthogonal symmetry class, one of the recently proposed nonstandard symmetry classes. For the nonzero torsional cases, we study two different models:(i) identical torsional term in the individual top (NZT-I model); (ii) non-identical torsional term due to their opposite sign in the individual top (NZT-II model). The NZT-I model has the permutation symmetry but no chiral symmetry; hence, this model is classified under the standard three-fold symmetry classes. On the other hand, the NZT-II model does not have permutation symmetry but has chiral symmetry; hence, this model is also classified as a nonstandard BDI symmetry class. In this study, we investigate the role of underlying symmetries on the entanglement between the two tops. Moreover, we explore the interrelations among classical phase space dynamics, energy transitions, and the entanglement between the tops.