Exactly Solvable Disorder-free Quantum Breakdown Model: Spectrum, Thermodynamics, and Dynamics

Abstract

We introduce and study a disorder-free version of the quantum breakdown model with all-to-all interactions. The Hamiltonian factorizes into the product of the zero-momentum-mode occupation number and a quadratic Hamiltonian including only pairing terms. This structure makes the model exactly solvable and produces an extensive zero-energy degeneracy. We obtain the spectrum and partition function in closed form and analyze the thermodynamics, spectral form factor, two-point functions, and a regulated out-of-time-ordered correlator (OTOC). The OTOC is time independent at leading order in the large-$N$ limit, while its time-dependent contributions first appear at order $1/N$. At infinite temperature, the time-dependent correction reduces to a two-point function arising from the zero-momentum component of the fermion operators. The model therefore provides a controlled setting for isolating the consequences of the breakdown interaction in the absence of disorder, spatial structure, and environmental coupling.

17 pages, 11 figures. Major revision with corrected numerical results and expanded analytical derivations