Nonperturbative functional renormalizationgroup approach to transport in the vicinity of a (2 +1 ) dimensional O(N )symmetric quantum critical point
Abstract
Using a nonperturbative functional renormalizationgroup approach to the twodimensional quantum O (N ) model, we compute the lowfrequency limit ω →0 of the zerotemperature conductivity in the vicinity of the quantum critical point. Our results are obtained from a derivative expansion to second order of a scaledependent effective action in the presence of an external (i.e., nondynamical) nonAbelian gauge field. While in the disordered phase the conductivity tensor σ (ω ) is diagonal, in the ordered phase it is defined, when N ≥3 , by two independent elements, σ_{A}(ω ) and σ_{B}(ω ) , respectively associated to SO (N ) rotations which do and do not change the direction of the order parameter. For N =2 , the conductivity in the ordered phase reduces to a single component σ_{A}(ω ) . We show that limω_{→0}σ (ω ,δ ) σ_{A}(ω ,δ ) /σ_{q}^{2} is a universal number, which we compute as a function of N (δ measures the distance to the quantum critical point, q is the charge, and σ_{q}=q^{2}/h the quantum of conductance). On the other hand we argue that the ratio σ_{B}(ω →0 ) /σ_{q} is universal in the whole ordered phase, independent of N and, when N →∞ , equal to the universal conductivity σ^{*}/σ_{q} at the quantum critical point.
 Publication:

Physical Review B
 Pub Date:
 January 2017
 DOI:
 10.1103/PhysRevB.95.014513
 arXiv:
 arXiv:1610.06476
 Bibcode:
 2017PhRvB..95a4513R
 Keywords:

 Condensed Matter  Strongly Correlated Electrons;
 Condensed Matter  Quantum Gases;
 Condensed Matter  Statistical Mechanics;
 High Energy Physics  Theory
 EPrint:
 25 pages, 4 figures