Disorder-free Quantum Breakdown Model: exact solution and dynamics

Non-equilibrium dynamics in quantum many-body systems is a central theme in modern physics. A canonical example is dielectric breakdown in insulators, where strong fields drive far-from-equilibrium evolution. Recently, Biao Lian proposed a quantum breakdown model in which disorder and the competition between the breakdown interaction and the chemical potential yield a crossover from many-body localization to quantum-chaotic behavior [1]. Motivated by this work, we isolate the role of the interaction by constructing a disorder-free, all-to-all variant of the model. Remarkably, this variant is exactly solvable and admits closed-form expressions for both real-time dynamics and thermodynamics (partition function and free energy) for arbitrary system sizes and temperatures. As chaos diagnostics, we compute the spectral form factor (SFF) and out-of-time-ordered correlators (OTOCs). The SFF relaxes directly to a plateau with no linear ramp, whereas the OTOCs display short-time exponential growth with a positive Lyapunov exponent. These results demonstrate that, even without disorder, the all-to-all interaction alone generates precursor signatures of quantum, which is consistent with what is observed in the disorder-free Sachdev–Ye–Kitaev model [2].

[1] Ozaki, S., & Katsura, H. (2024). arXiv:2402.13154.

[2] Lian, B. (2023). Phys. Rev. B, 107(11), 115171.