1. Emergence of a control parameter for the antiferromagnetic quantum critical metal
- Author
-
Andres Schlief, Peter Lunts, and Sung-Sik Lee
- Subjects
Large class ,Physics ,Strongly Correlated Electrons (cond-mat.str-el) ,Infrared fixed point ,FOS: Physical sciences ,02 engineering and technology ,021001 nanoscience & nanotechnology ,01 natural sciences ,Metal ,Condensed Matter - Strongly Correlated Electrons ,Exact solutions in general relativity ,Singularity ,Quantum mechanics ,visual_art ,0103 physical sciences ,visual_art.visual_art_medium ,Antiferromagnetism ,010306 general physics ,0210 nano-technology ,Critical exponent ,Quantum - Abstract
We study the antiferromagnetic quantum critical metal in $3-\epsilon$ 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 $\epsilon$-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 (IR) fixed point, and the $\epsilon$-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 $\epsilon$ in the limit that the ratio of velocities vanishes. The $\epsilon$-expansion gives critical exponents which are consistent with the exact solution obtained in $0 < \epsilon \leq 1$., Comment: 20 pages, 8 figures; ver2: minor corrections, comparison to ferromagnetic quantum criticality added, typos fixed, references added
- Published
- 2017
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