Integrability-controlled confinement transition

Determine whether the fast-scrambling-to-operator-confinement transition in auxiliary-qubit-coupled spin chains can be tuned directly by integrability, including in spin-conserving chains coupled to an ancilla or in systems with explicit disorder in bonds or local fields.

Background

The paper demonstrates that coupling a mixed-field Ising spin chain to an auxiliary qubit produces a crossover between ancilla-accelerated, super-ballistic scrambling at weak coupling and sub-ballistic operator confinement at strong coupling. The authors note that this crossover persists whether the bare chain is integrable or nonintegrable because the ancilla coupling itself generally breaks integrability.

The unresolved problem is to determine whether integrability can serve as a direct tuning parameter for the transition, rather than merely modifying a transition generated by the auxiliary coupling. The proposed settings include spin-conserving chains coupled to an ancilla and systems with explicit disorder in bonds or local fields.