Activity leads to topological phase transition in 2D populations of heterogeneous oscillators

Populations of heterogeneous, noisy oscillators on a two-dimensional lattice display short-range order. Here, we show that if the oscillators are allowed to actively move in space, the system undergoes instead a Berezenskii-Kosterlitz-Thouless transition and exhibits quasi-long-range order. This fundamental result connects two paradigmatic models -- XY and Kuramoto model -- and provides insight on the emergence of order in active systems.