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

Kinya Guan; Hosho Katsura

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arXiv · 2603.17379

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

Kinya Guan·Hosho Katsura

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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.

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Kinya Guan, Hosho Katsura. 2026-03-18. Exactly Solvable Disorder-free Quantum Breakdown Model: Spectrum, Thermodynamics, and Dynamics. https://arxiv.org/abs/2603.17379

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