Thermally induced localization of dopants in a magnetic spin ladder

I unveil a novel variant of Anderson localization. This emergent phenomenon pertains to the motion of a dopant in a thermal spin lattice, rendered localized by thermal fluctuations. This is in stark contrast to the intrinsic origin of localization for quenched disorder. The system of interest consists of spin-1/2 particles organized in a two-leg ladder with nearest neighbor Ising interactions J. The motion of a hole – the dopant – is initialized by suddenly removing a spin from the thermal spin ensemble, which then moves along the ladder via nearest neighbor hopping t. I find that the hole remains localized for all values of J/t and for all nonzero temperatures. The origin is an effective disorder potential seen by the hole and induced by thermal spin fluctuations. For ferromagnetic couplings (J < 0), the associated localization length of the hole increases with decreasing temperature and becomes proportional to the correlation length at low temperatures. For antiferromagnetic couplings (J > 0), there is a smooth crossover between thermal localization at high temperatures to localization driven by the antiferromagnetic order at low temperatures. Finally, I analyze a setup with Rydberg-dressed atoms, which naturally realizes finite range Ising interactions, accessible in current experimental setups. I show that the discovered localization phenomenon can be probed on experimentally accessible length- and timescales, providing a strong testing ground for my predictions.