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Operator growth and Krylov construction in dissipative open quantum systems
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Operator growth and Krylov construction in dissipative open quantum systems
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Inspired by the universal operator growth hypothesis, we extend the formalism of Krylov construction in dissipative open quantum systems connected to a Markovian bath. Our construction is based upon the modification of the Liouvillian superoperator by the appropriate Lindbladian, thereby following the vectorized Lanczos algorithm and the Arnoldi iteration. This is well justified due to the incorporation of non-Hermitian effects due to the environment. We study the growth of Lanczos coefficients in the transverse field Ising model (integrable and chaotic limits) for boundary amplitude damping and bulk dephasing. Although the direct implementation of the Lanczos algorithm fails to give physically meaningful results, the Arnoldi iteration retains the generic nature of the integrability and chaos as well as the signature of non-Hermiticity through separate sets of coefficients (Arnoldi coefficients) even after including the dissipative environment. Our results suggest that the Arnoldi iteration is meaningful and more appropriate in dealing with open systems.
Forward citations
Cited by 5 Pith papers
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The Geometry of Quantum Complexity in Open Systems
Nielsen complexity for Lindbladian open systems induces a sub-Finslerian geometry on mixed states whose flag curvature depends on control penalty factors.
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In W3 CFTs, Lanczos coefficients b_N grow as N^2 for generalized Liouvillian with W generators, violating the universal linear growth bound and causing divergent Krylov complexity, with the same quadratic growth in th...
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Generalized Krylov complexity predicts the minimum time to realize target operations in analog quantum simulators such as Rydberg atom arrays.
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Derivative of Krylov spread complexity diverges logarithmically at SSH topological transitions and is bounded by fidelity susceptibility in general two-band Hamiltonians, with a non-unitary duality between phases.
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Krylov complexity equals Fubini-Study volume for closed and open two-mode squeezed states, providing analytic support for the generalized CV conjecture via information geometry.
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