Figure 2: Scaling laws of contact determined by the universality class of the phase transition in the quantum critical region.

The left panels show the temperature-scaled contact , where t=T/ε_b is the dimensionless temperature, as a function of the chemical potential near the phase boundaries V–P (a) and F–PP (b), respectively. Curves at different temperatures intersect at the quantum critical point as predicted by equation (15). The right panels show that the rescaled contact versus temperature-scaled chemical potential at different temperatures collapse into a single line, characteristic of critical behaviour in the quantum critical region. These data collapses confirm the critical dynamic exponent z=2 and correlation length exponent ν=1/2 in terms of the universal scaling in equation (15).