Integrable nonunitary open quantum circuits

Abstract

We explicitly construct an integrable and strongly interacting dissipative quantum circuit via a trotterization of the Hubbard model with imaginary interaction strength. To prove integrability, we build an inhomogeneous transfer matrix, from which conserved superoperator charges can be derived, in particular, the circuit's dynamical generator. After showing the trace preservation and complete positivity of local maps, we reinterpret them as the Kraus representation of the local dynamics of free fermions with single-site dephasing. The integrability of the map is broken by adding interactions to the local coherent dynamics or by removing the dephasing. In particular, even circuits built from convex combinations of local free-fermion unitaries are nonintegrable. Moreover, the construction allows us to explicitly build circuits belonging to different non-Hermitian symmetry classes, which are characterized by the behavior under transposition instead of complex conjugation. We confirm all our analytical results by using complex spacing ratios to examine the spectral statistics of the dissipative circuits.

10 pages, 2 figures. v2: some additional details, as published

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• Universality and its limits in non-Hermitian many-body quantum chaos using the Sachdev-Ye-Kitaev model
• Introduction to classical and quantum integrability
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• Krylov complexity and Trotter transitions in unitary circuit dynamics
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• Exactly solvable dissipative dynamics and one-form strong-to-weak spontaneous symmetry breaking in interacting two-dimensional spin systems
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• Brick Wall Quantum Circuits with Global Fermionic Symmetry
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