Entanglement entropy of highly excited eigenstates of SU(2) symmetric systems

It has been recently conjectured that the average entanglement entropy of highly excited eigenstates of many-body Hamiltonians can be used as a diagnostic of quantum chaos and integrability [1]. In quantum chaotic systems, the leading term exhibits a volume-law behavior with a constant coefficient, while in integrable systems the leading term exhibits a volume-law behavior with a coefficient that depends on the ratio between the sizes of the subsystem and the entire system [2]. Furthermore, in quantum chaotic systems, the first subleading correction has been found to signal the presence of conservation laws such as particle-number [3] and energy [4] conservation. In this work, we study the entanglement entropy of highly excited eigenstates of SU(2) symmetric systems to unveil the effect of noncommuting conservation laws. We show that while such a symmetry does not change the leading order behavior of the entanglement entropy, it does change the subleading corrections. We discuss the nature of those changes using numerical and analytical calculations.

[1] T. LeBlond, K. Mallayya, L. Vidmar, and M. Rigol, Phys. Rev. E 100, 062134 (2019).

[2] E. Bianchi, L. Hackl, M. Kieburg, M. Rigol, and L. Vidmar, PRX Quantum 3, 030201 (2022).

[3] L. Vidmar and M. Rigol, Phys. Rev. Lett. 119, 220603 (2017).

[4] C. Murthy and M. Srednicki, Phys. Rev. E 100, 022131 (2019).