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

TL;DR

This paper introduces an exactly solvable, disorder-free quantum model with all-to-all interactions, analyzing its spectral, thermodynamic, and dynamical properties, including unique features in OTOC growth.

Contribution

It presents a novel, exactly solvable quantum breakdown model without disorder, revealing its spectral and dynamical characteristics in detail.

Findings

Large set of zero-energy states identified

Distinct early-time OTOC growth regime observed

Spectral form factor shaped by factorized structure

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.