Magnetic field induced symmetry breaking in nonequilibrium quantum networks

Thingna, Juzar; Manzano, Daniel; Cao, Jianshu

doi:10.48550/arxiv.1909.09549

Cited by 2 publications

(2 citation statements)

References 39 publications

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“…As illustrative examples, we apply our theory to three archetypal models: a quantum network, the open randomly dissipative XXX Heisenberg model and the spin-dephased Fermi-Hubbard model. The models are interesting for understanding transport in molecules and quantum networks [26,39], the effects of disorder on relaxation, and out-of-equilibrium superconductivity [40]. We also study the XXX model under collective dissipation as a simple toy example.…”

Section: Introductionmentioning

confidence: 99%

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

Zhang

Tindall

Mur-Petit

et al. 2020

J. Phys. A: Math. Theor.

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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.

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Section: Introductionmentioning

confidence: 99%

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

Zhang

Tindall

Mur-Petit

et al. 2020

J. Phys. A: Math. Theor.

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“…This size is even more reduced if the Hamiltonian posses additional symmetries, see below. This can prove useful for exact diagonalization studies of small spin clusters, which can be of interest for understanding magnetic response of correlated materials [19] (for alternative ways of accounting for symmetries see [15,20]).…”

Section: System Of Spins 1/2 With the Heisenberg Interactionmentioning

confidence: 99%

Merits of using density matrices instead of wave functions in the stationary Schrödinger equation for systems with symmetries

Shpagina¹,

Uskov²,

Ильин³

et al. 2020

J. Phys. A: Math. Theor.

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The stationary Schrödinger equation can be cast in the form Hρ = Eρ, where H is the system's Hamiltonian and ρ is the system's density matrix. We explore the merits of this form of the stationary Schrödinger equation, which we refer to as SSEρ, applied to many-body systems with symmetries. For a nondegenerate energy level, the solution ρ of the SSEρ is merely a projection on the corresponding eigenvector. However, in the case of degeneracy ρ in nonunique and not necessarily pure. In fact, it can be an arbitrary mixture of the degenerate pure eigenstates. Importantly, ρ can always be chosen to respect all symmetries of the Hamiltonian, even if each pure eigenstate in the corresponding degenerate multiplet spontaneously breaks the symmetries. This and other features of the solutions of the SSEρ can prove helpful by easing the notations and providing an unobscured insight into the structure of the eigenstates. We work out the SSEρ for the system of spins 1/2 with Heisenberg interactions. Eigenvalue problem for quantum observables other than Hamiltonian can also be formulated in terms of density matrices. We provide an analytical solution to one of them, S 2 ρ = S(S + 1)ρ, where S is the total spin of N spins 1/2, and ρ is chosen to be invariant under permutations of spins. This way we find an explicit form of projections to the invariant subspaces of S 2 . Finally, we note that the anti-Hermitian part of the SSEρ can be used to construct sum rules for temperature correlation functions, and provide an example of such sum rule. 03J 12 3J 23 3J 13 J 12 −2J 12 J 23 J 13 J 23 J 12 −2J 23 J 13 J 13 J 12 J 23 −2J 13

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Magnetic field induced symmetry breaking in nonequilibrium quantum networks

Cited by 2 publications

References 39 publications

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

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

Merits of using density matrices instead of wave functions in the stationary Schrödinger equation for systems with symmetries

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