Hyperscaling violation at the Isingnematic quantum critical point in twodimensional metals
Abstract
Understanding optical conductivity data in the optimally doped cuprates in the framework of quantum criticality requires a strongly coupled quantum critical metal which violates hyperscaling. In the simplest scaling framework, hyperscaling violation can be characterized by a single nonzero exponent θ , so that in a spatially isotropic state in d spatial dimensions, the specific heat scales with temperature as T^{(d θ )/z}, and the optical conductivity scales with frequency as ω^{(d θ 2 )/z} for ω ≫T , where z is the dynamic critical exponent defined by the scaling of the fermion response function transverse to the Fermi surface. We study the Isingnematic critical point, using the controlled dimensional regularization method proposed by Dalidovich and Lee [Phys. Rev. B 88, 245106 (2013), 10.1103/PhysRevB.88.245106]. We find that hyperscaling is violated, with θ =1 in d =2 . We expect that similar results apply to Fermi surfaces coupled to gauge fields in d =2 .
 Publication:

Physical Review B
 Pub Date:
 July 2016
 DOI:
 10.1103/PhysRevB.94.045133
 arXiv:
 arXiv:1605.00657
 Bibcode:
 2016PhRvB..94d5133E
 Keywords:

 Condensed Matter  Strongly Correlated Electrons;
 Condensed Matter  Quantum Gases;
 High Energy Physics  Theory
 EPrint:
 28 pages