Quantum spin chains and ladders are the source of an extremely rich physics. As with any one dimensional system, topological transitions are the norm rather than the exception and many phenomena are controlled by the Berezinski-Kosterlitz-Thouless (BKT) phase transition. Studying quantitatively these phenomena is however usually difficult and one relies on asymptotic solutions, such as field theory ones provided by the bosonization technique. I will show how using a combination of analytics and numerical techniques (time dependent DMRG) one can get a very precise solutions of these problems at all scales. Using these techniques one is now in position to tackle more complex phase transitions and I will discuss the recently analyzed case of an unusual topological phase transition, described by the dual field double sine-Gordon model, that occurs in the BaCoVO compound [1]

[1]  Quentin Faure, Shintaro Takayoshi et al.  Nature Physics 14, 716–722 (2018)