Thermal states emerging from low-entanglement background in disordered spin models

Abstract: Thermalization in isolated quantum systems is governed by the eigenstate thermalization hypothesis, while strong disorder can induce its breakdown via many-body localization. Here we show that disorder can also generate a narrow band of thermal eigenstates embedded in an otherwise non-thermal spectrum. We illustrate this generic mechanism using paradigmatic spin-1 models, including Heisenberg, XY, and Affleck-Kennedy-Lieb-Tasaki (AKLT) models with several types of disorder. By analyzing their level statistics, entanglement properties and quench dynamics, we show that the disorder-induced states are genuinely thermal and we trace their origin to the null space of the disorder term in the Hamiltonian. Our results demonstrate that disorder can give rise to an unexpected coexistence of thermal and non-thermal dynamics within the same many-body spectrum.