Résumé
The Berezinskii-Kosterlitz-Thouless (BKT) transition provides a remarkable example of a transition controlled by topological effects. In addition to its consequences for classical two-dimensional systems, the BKT transition directly applies to one-dimensional quantum problems as well. It was shown in this seminar how, using a formalism initially developed by Haldane, one can relate the BKT problem to another paradigmatic quantum problem, namely the so-called sine-Gordon theory. This mapping allows one to derive several interesting consequences both for clean (in periodic or quasi-periodic lattices) and dirty bosons. Such problems were examined in the seminar, in particular in the context of cold atomic gases. It was also shown how using this mapping one can go back to the case of two dimensional systems, namely disordered superconducting films.
