The Berezinskii-Kosterlitz-Thouless (BKT) transition is a topological phase transition in 2D superfluids. Below T_BKT, vortex-antivortex pairs bind and superfluid stiffness is finite. Above T_BKT, pairs unbind, and the system becomes normal.
BKT transition: In 2D, long-range order is forbidden (Mermin-Wagner theorem), but the XY model has a topological transition. Vortex-antivortex pairs interact logarithmically: E_pair = 2E_c + (J/π)ln(r/a). Pairs bind below T_BKT = πJ/2. At T_BKT⁻, the superfluid stiffness jumps discontinuously: ρ_s(T_BKT⁻) = (2/π)T_BKT (universal jump). Above T_BKT, free vortices proliferate and ρ_s → 0. Left: XY phase field θ(x,y) with bound/free vortex pairs. Right: ρ_s vs T curve with the Nelson-Kosterlitz universal jump.