Stationary state degeneracy of open quantum systems with non-abelian symmetries

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 fullyconnected 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.Submitted to: J. Phys. A: Math. Theor.

Fluctuations of work in realistic equilibrium states of quantum systems with conserved quantities

“…This points to the importance of the role of charges in realistic non-equilibrium processes, such as equilibration in quasi-integrable systems [24], and dissipation and relaxation in driven systems with conservation laws [42,43]. A case of particular theoretical interest for future exploration arises when the charges supported by the Hamiltonian do not commute with each other [25,[44][45][46][47]. Our results also call attention to the relevance of charges in the work statistics of realistic cyclic processes where the system is driven to an intermediate state with charges, an issue that may be exploited to design more efficient quantum engines [48][49][50][51].…”

Qubit Decoherence and Symmetry Restoration through Real-Time Instantons

“…Open quantum systems subject simultaneously to dissipative effects and a strong external drive obey effective dynamics described by the Lindblad equation [1][2][3][4][5][6]. Such systems have gained attention for their ability to realize multiple non-equilibrium steady states [7][8][9][10][11][12][13][14]. Of particular interest are systems exhibiting quantum bi-stability, in which the space of steady states has the structure of a Bloch sphere and can be used to encode a qubit stably in contact with its environment [15][16][17].…”

“…The stationary states of a Lindblad equation are determined by its symmetries [7,10]; the spontaneous breaking of symmetry can lead to bi-stability [11]. A broken 'strong' symmetry (in the sense of Ref.…”

Exact solutions of interacting dissipative systems via weak symmetries

“…Turning to dissipative (open) quantum systems, the situation becomes more subtle, as the non-unitary nature of the evolution makes the link between symmetry and conservation laws less direct (see, e.g. [1][2][3][4][5][6]). In the typical case of a Markovian system described by a Lindblad master equation, one often has only a so-called "weak symmetry" [3].…”