Liouvillian Kramers Degeneracy

Abstract

The Kramers theorem generally guarantees the spectral degeneracy of time-reversal-invariant Hamiltonian operators with half-integer spin, underlying a variety of physical phenomena. Despite its fundamental significance, the Kramers degeneracy has been argued to be absent in Liouvillian superoperators acting on mixed states because of the double structure of the Hilbert space. Here, we instead demonstrate that the interplay of time-reversal symmetry$^†$ and parity symmetry enforces the Kramers degeneracy in Liouvillians. We explicitly construct dissipative many-body models of interacting fermions and spins exhibiting the Kramers degeneracy and show that their complex spectral statistics follow those of non-Hermitian random matrices in the corresponding symplectic symmetry classes. Of the three fundamental universality classes of non-Hermitian random matrices, the symplectic class has never been realized in symmetry-resolved many-body Liouvillians. Our constructions provide its explicit realizations and spectral signatures of nonintegrability in symplectic open quantum systems.