Stationary State Degeneracy of Open Quantum Systems with Non-Abelian Symmetries
| Autor: | Dieter Jaksch, Berislav Buča, Joseph Tindall, Jordi Mur-Petit, Zhao Zhang |
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| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
Atomic Physics (physics.atom-ph) General Physics and Astronomy FOS: Physical sciences 01 natural sciences Physics - Atomic Physics 010305 fluids & plasmas symbols.namesake Theoretical physics 0103 physical sciences 010306 general physics Quantum Condensed Matter - Statistical Mechanics Mathematical Physics Physics Quantum Physics Quantum network Statistical Mechanics (cond-mat.stat-mech) Hilbert space Statistical and Nonlinear Physics Mathematical Physics (math-ph) Invariant (physics) Linear subspace Quantum Gases (cond-mat.quant-gas) Modeling and Simulation Irreducible representation symbols Condensed Matter - Quantum Gases Degeneracy (mathematics) Quantum Physics (quant-ph) Stationary state |
| DOI: | 10.48550/arxiv.1912.12185 |
| Popis: | 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. Comment: 19 pages, 3 figures, 3 tables |
| Databáze: | OpenAIRE |
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