Integrable deformations of superintegrable quantum circuits

Abstract

Superintegrable models are very special dynamical systems: they possess more conservation laws than what is necessary for complete integrability. This severely constrains their dynamical processes, and it often leads to their exact solvability, even in non-equilibrium situations. In this paper we consider special Hamiltonian deformations of superintegrable quantum circuits. The deformations break superintegrability, but they preserve integrability. We focus on a selection of concrete models and show that for each model there is an (at least) one parameter family of integrable deformations. Our most interesting example is the so-called Rule54 model. We show that the model is compatible with a one parameter family of Yang-Baxter integrable spin chains with six-site interaction. Therefore, the Rule54 model does not have a unique integrability structure, instead it lies at the intersection of a family of quantum integrable models.

20 pages, 6 figures, v2: minor changes, Mathematica notebook uploaded, v3: references added, v4: minor modifications, v5: minor modifications

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Cited by in corpus (10)

• Microscopic origin of the quantum Mpemba effect in integrable systems
• Dynamics of charge fluctuations from asymmetric initial states
• Non-equilibrium dynamics of charged dual-unitary circuits
• Non-equilibrium dynamics of symmetry-resolved entanglement and entanglement asymmetry: Exact asymptotics in Rule 54
• Exactly solvable many-body dynamics from space-time duality
• Quantum Zeno Effect in Noisy Integrable Quantum Circuits for Impurity Models
• Integrability and charge transport in asymmetric quantum-circuit geometries
• Geometric representations of braid and Yang-Baxter gates
• Probes of Full Eigenstate Thermalization in Ergodicity-Breaking Quantum Circuits
• Phase transition from localization to chaos in classical many-body system