Superuniversal Transport Near a Quantum Critical Point

by Tommy on 12/05/2017

This paper was difficult to get through but contained a surprise at the end.

Superuniversal transport near a (2+1)-dimensional quantum critical point, Félix Rose and Nicolas Dupuis (10 May 2017)

We compute the zero-temperature conductivity in the two-dimensional quantum O(N) model using a nonperturbative functional renormalization-group approach. At the quantum critical point we find a universal conductivity σ∗/σQ (with σQ=q2/h the quantum of conductance and q 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 N≥3, by two independent elements, σA(ω) and σB(ω), respectively associated to O(N) rotations which do and do not change the direction of the order parameter. Whereas σA(ω→0) corresponds to the response of a superfluid (or perfect inductance), the numerical solution of the flow equations shows that limω→0σB(ω)/σQ=σ∗B/σQ is a superuniversal (i.e. N-independent) constant. These numerical results, as well as the known exact value σ∗B/σQ=π/8 in the large-N limit, allow us to conjecture that σ∗B/σQ=π/8 holds for all values of N, a result that can be understood as a consequence of gauge invariance and asymptotic freedom of the Goldstone bosons in the low-energy limit.

This is a nightmare of html formatting so you’ll just have to read the paper like I did.

It will be well worth your time if you’re interested in this kind of thing. Like I am.

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