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arXiv · 1912.12185

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

Zhao Zhang·Joseph Tindall·Jordi Mur-Petit·Dieter Jaksch·Berislav Buča
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Abstract

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. Moreover, our work provides a theory for the systematic block-decomposition of a Liouvillian with non-Abelian symmetries, reducing the computational difficulty involved in diagonalising these objects and exposing a natural, physical structure to the steady states - which we observe in our examples.

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Zhao Zhang, Joseph Tindall, Jordi Mur-Petit, Dieter Jaksch, Berislav Buča. 2019-12-27. Stationary State Degeneracy of Open Quantum Systems with Non-Abelian Symmetries. https://doi.org/10.1088/1751-8121%2Fab88e3

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