Deconfined quantum criticality

In this work it is studied a type of quantum phase transitions beyond the Landau-Ginzburg-Wilson (LGW) paradigm. In particular it is described a second order transition between the Nèel and the Valence Bond Solid (VBS) states for a two dimensional quantum square lattice with antiferromagnetic interactions. The natural description of this critical theory is not given in terms of the order parameter, but in terms of an emergent gauge field which mediates interactions between "fractional" particles. These particles are confined on either sides of the transition, while they emerge at the critical point, that is thus called "deconfined". This critical theory corresponds to that of a 3D classical O(3) model with monopoles suppressed. In the second part of this work, this model is numerically simulated by using Monte Carlo methods, and its critical exponents are obtained.