An application of renormalization in Hilbert space at phase transition points in strongly interacting systems

We introduce an algorithm aimed to reduce the dimensions of Hilbert space. It is used here in order to study the behaviour of low energy states of strongly interacting quantum many-body systems at first order transitions and avoided crossings. The method is tested on different frustrated quantum spin ladders with two legs. The role and importance of symmetries are investigated by using different bases of states.