The Berezinskii-Kosterlitz-Thouless (BKT) transition is the paradigmatic example of a topological phase transition without symmetry breaking, where a quasiordered phase, characterized by a power-law scaling of the correlation functions at low temperature, is disrupted by the proliferation of topological excitations above the critical temperature

T_{BKT}

. In this Letter, we consider the effect of long-range decaying couplings

\sim r^{- 2 - σ}

on the BKT transition. After pointing out the relevance of this nontrivial problem, we discuss the phase diagram, which is far richer than the corresponding short-range one. It features—for

7 / 4 < σ < 2

—a quasiordered phase in a finite temperature range

T_{c} < T < T_{BKT}

, which occurs between a symmetry broken phase for

T < T_{c}

and a disordered phase for

T > T_{BKT}

. The transition temperature

T_{c}

displays unique universal features quite different from those of the traditional, short-range

X Y

model. Given the universal nature of our findings, they may be observed in current experimental realizations in 2D atomic, molecular, and optical quantum systems.

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