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 a large set of zero-energy states. We analyze its spectral, thermodynamic, and dynamical properties. In particular, we show how the factorized structure shapes the spectral form factor and the real-time dynamics. We also compute two-point functions and out-of-time-ordered correlators (OTOCs), and find a distinct early-time growth regime in the OTOCs. These results provide a solvable setting in which spectral properties and real-time dynamics can be analyzed in a controlled way in the absence of disorder, spatial structure, and environmental coupling.

Figures (11)

• Figure 1: Schematic illustration of the disorder-free all-to-all quantum breakdown model. A single site contains $N$ fermionic modes, and the interaction couples them uniformly with strength $J=1$.
• Figure 2: Spectrum for $N=10$. The extensive zero-energy plateau receives contributions from both the frozen and active sectors, while the nonzero spectrum arises from the active sector.
• Figure 3: Infinite-temperature SFF $g(t,0)$ for several system sizes $N$. Solid lines show the numerical results, while dashed lines show the small-$t$ expansion in Eq. \ref{['eq:g_small_t_main']}.
• Figure 4: Finite-temperature SFF $g(t,\beta)$ for $N=50$ at several $\beta$. The behavior shows oscillatory revivals rather than a clear ramp, and the revival peaks can vary irregularly in height.
• Figure 5: Free energy density $|F(T)|/N$ as a function of $T=1/\beta$ in the high-temperature regime. The numerical data (computed for $N=19,199,1999$) approach the analytic line $T\log 2$ for large $T$.