Superuniversal transport near a -dimensional quantum critical point
F. Rose and N. Dupuis
Phys. Rev. B 96, 100501(R) (2017) - Published 11 September, 2017
We compute the zero-temperature conductivity in the two-dimensional quantum model using a nonperturbative functional renormalization-group approach. At the quantum critical point we find a universal conductivity (with the quantum of conductance and the charge) in reasonable quantitative agreement with quantum Monte Carlo simulations and conformal bootstrap results. In the ordered phase the conductivity tensor is defined, when , by two independent elements, and , respectively associated with rotations which do and do not change the direction of the order parameter. Whereas corresponds to the response of a superfluid (or perfect inductance), the numerical solution of the flow equations shows that is a superuniversal (i.e., -independent) constant. These numerical results, as well as the known exact value in the large- limit, allow us to conjecture that holds for all values of , a result that can be understood as a consequence of gauge invariance and asymptotic freedom of the Goldstone bosons in the low-energy limit.
