Theoretical analysis of the Berezinskii–Kosterlitz–Thouless transition critical dynamics near the zero temperature

The Berezinskii–Kosterlitz–Thouless (BKT) phase transition is considered in the condition of lowest temperatures, when thermal fluctuations give place to quantum ones. For this goal, the critical dynamic of the 2D XY-model near the quantum critical point is considered. The approach based on the Keldysh–Schwinger technique of non-equilibrium dynamics description is used, as well as the method of taking into account the crossover from the thermal fluctuation regime to the quantum one in the renormalization group technique. For the system with low vortex concentration, it is shown that the BKT transition unavoidably occurs at a temperature above the crossover temperature from the thermal fluctuation regime to the quantum one. As a result, at small temperatures the critical exponent of the BKT transition, η = 1 / 4 , remains unchanged, and however, the universal relation of the superfluid density jump adjusts a little from the well-known relation by Nelson and Kosterlitz (Phys. Rev. Lett. 39:19, 1977).