Entanglement entropy and critical behaviour of disordered spin ladders tending towards two dimensions

Quenched disorder has a profound effect on the low-energy, low-temperature and long wavelength properties of quantum systems. As a consequence, the quantum phase transition of the random transverse field Ising (RTFI) model is described by a so-called infinite-randomness fixed point. For the one dimensional chain geometry many exact and numerical results are known, in contrast with the higher dimensional case. We studied the RTFI model on ladder geometries with two and more legs tending towards two dimensions using the strong disorder renormalization group method numerically. The location of the critical points and the critical exponents are obtained. From the shift of the critical points, the v correlation length exponent of the two dimensional case can be calculated too. Moreover, we studied the asymptotic scaling of the entanglement in these systems based on the von Neumann entropy, from which the effective central charge is calculated. (authors)