Eigenstate thermalization in spin-½ chains with SU(2) symmetry

The effects of non-commuting conserved quantities in entanglement, thermalization, and quantum thermodynamics have attracted significant attention in recent years. Motivated by those studies, the eigenstate thermalization hypothesis (ETH) was recently generalized to account for non-Abelian charges [1]. In this work, we study eigenstate thermalization in the extended spin-½ Heisenberg chain, which exhibits non-Abelian SU(2) symmetry. We consider two observables directly connected to different spherical tensors, an SU(2) invariant observable, which connects states within the same total spin sector, and an observable that breaks SU(2) symmetry and as such connects states that belong to different total spin sectors. Focusing on the zero total magnetization sector, we find that the observables we consider satisfy the non-Abelian ETH away from integrability.

References:

[1] C. Murthy, A. Babakhani, F. Iniguez, M. Srednicki, and N. Yunger Halpern, Non-abelian eigenstate thermalization hypothesis, Phys. Rev. Lett. 130, 140402 (2023).