A quantum particle on a lattice with a linear potential — a tilt that increases the energy of each site by a fixed amount — cannot spread. Unlike Anderson localization, which requires disorder to confine wavefunctions, Stark localization is caused by the potential gradient itself. The eigenstates are not just exponentially localized but superexponentially localized: their tails fall off faster than any exponential, confined to a handful of sites regardless of the lattice size. The single-particle case is exactly solvable, and the localization is complete.
The question is what happens when you add more particles and let them interact. The conventional expectation from many-body physics is that interactions destroy localization. Anderson localization — confinement by disorder — is rigorously established for single particles but believed to break down when interactions are included, with the system eventually thermalizing and losing memory of its initial configuration. Many-body localization, the interacting generalization, remains controversial: some numerical evidence supports it, but the current theoretical consensus leans toward eventual thermalization for generic interacting disordered systems, at least in dimensions above one.
De Roeck, Hannani, Lerose, and Vandenbosch (arXiv 2602.23352, February 2026) prove that Stark localization is different. They show that superexponential spectral localization persists for any number of interacting particles and any interaction strength. The result is not numerical or approximate — it is a mathematical proof.
The proof works because the linear potential creates a fundamentally different localization mechanism from disorder. In Anderson localization, the random potential creates resonances between distant sites that happen to have similar energies. Interactions can bridge these resonances, providing pathways for the system to explore its Hilbert space and thermalize. In Stark localization, there are no accidental resonances. The energy difference between sites separated by distance d grows linearly with d, and the tunneling amplitude falls off at least exponentially with d. For any finite interaction strength, the interaction cannot overcome the energy gradient at sufficient distance. The tilt wins everywhere, not just at typical sites.
The superexponential localization is preserved because the Wannier-Stark eigenstates of the single-particle problem have tails that decrease faster than the interaction can correlate. Adding interactions perturbs these states but cannot delocalize them, because the perturbation theory converges — the energy denominators grow with distance faster than the matrix elements. This convergence holds for every number of particles, not just for two or three, because the N-body energy differences still grow linearly with the spatial extent of the configuration.
The contrast with the disordered case is sharp. Disorder creates a random energy landscape with rare resonances whose density can overwhelm localization as the system size grows. The linear potential creates a deterministic energy landscape with no resonances at any scale. Interactions cannot exploit what isn't there. The stability of Stark localization is not fragile resistance to perturbation — it is structural immunity to the mechanism that destroys other forms of localization.