Emergence of a control parameter for the antiferromagnetic quantum critical metal
Peter Lunts, Andrés Schlief, Sung-Sik Lee
We study the antiferromagnetic quantum critical metal in $3\ensuremath{-}\ensuremath{\epsilon}$ space dimensions by extending the earlier one-loop analysis [Sur and Lee, Phys. Rev. B 91, 125136 (2015)] to higher-loop orders. We show that the $\ensuremath{\epsilon}$ expansion is not organized by the standard loop expansion, and a two-loop graph becomes as important as one-loop graphs due to an infrared singularity caused by an emergent quasilocality. This qualitatively changes the nature of the infrared fixed point, and the $\ensuremath{\epsilon}$ expansion is controlled only after the two-loop effect is taken into account. Furthermore, we show that a ratio between velocities emerges as a small parameter, which suppresses a large class of diagrams. We show that the critical exponents do not receive corrections beyond the linear order in $\ensuremath{\epsilon}$ in the limit that the ratio of velocities vanishes. The $\ensuremath{\epsilon}$ expansion gives critical exponents which are consistent with the exact solution obtained in $0<\ensuremath{\epsilon}\ensuremath{\le}1$.
arXiv:1701.08218•Physical review. B./Physical review. B•Jun 8, 2017•31 citations