Stationary State Degeneracy of Open Quantum Systems with Non-Abelian Symmetries

Understand

We study the null space degeneracy of open quantum systems with multiple non-Abelian, strong symmetries.

• By decomposing the Hilbert space representation of these symmetries into an irreducible representation involving the direct sum of multiple, commuting, invariant subspaces we derive a tight lower bound for the stationary state degeneracy.
• We apply these results within the context of open quantum many-body systems, presenting three illustrative examples: a fully-connected quantum network, the XXX Heisenberg model and the Hubbard model.
• We find that the derived bound, which scales at least cubically in the system size the $SU(2)$ symmetric cases, is often saturated.