Integrable nonunitary open quantum circuits
- URL: http://arxiv.org/abs/2011.06565v2
- Date: Fri, 19 Mar 2021 17:00:13 GMT
- Title: Integrable nonunitary open quantum circuits
- Authors: Lucas S\'a, Pedro Ribeiro, and Toma\v{z} Prosen
- Abstract summary: We explicitly construct an integrable and strongly interacting dissipative quantum circuit via a trotterization of the Hubbard model with imaginary interaction strength.
The construction allows us to explicitly build circuits belonging to different non-Hermitian symmetry classes.
- Score: 0.9290757451344674
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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.
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