Physics and Astronomy Colloquium

The universal properties that appear in the proximity of a second order phase transition are determined by a few relevant properties. The spatial dimensionality is one of them. It determines whether a phase transition is allowed to take place and, if that is the case, influences the values of critical exponents. In this talk I will demonstrate that the spatial dimensionality of a quantum critical point can be reduced when the system is governed by an emergent symmetry, i.e. when the ground state has higher symmetry than the Hamiltonian. This is demonstrated to be the case for magnetic field tuned quantum critical points in frustrated spin systems. The critical fluctuations of a three dimensional spin system on a body centered tetragonal lattice are shown to be strictly two dimensional, explaining the peculiar high magnetic field behavior of BaCuSi2O6. The mapping of the problem onto a chemical potential tuned Bose-Einstein condensation at T=0 illustrates the generality of the mechanism for dimensionality reduction at quantum critical points.