Phase Transition of Bipartite Entanglement

By applying general methods of statistical mechanics, we analyze the distribution of the Schmidt coefficients of the reduced density matrix of a quantum system in a pure state. By introducing a fictitious temperature and a partition function, the problem is translated in terms of the distribution of the eigenvalues of random matrices. We investigate the appearance of two phase transitions, one at a positive temperature, associated with very entangled states, and one at a negative temperature, signaling the appearance of a significant factorization in the many-body wave function.