Large- N theory of critical Fermi surfaces
| Autor: | Subir Sachdev, Haoyu Guo, Aavishkar A. Patel, Ilya Esterlis |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Condensed Matter::Quantum Gases
High Energy Physics - Theory Physics Coupling constant Strongly Correlated Electrons (cond-mat.str-el) Condensed matter physics Physical system FOS: Physical sciences Fermi surface 02 engineering and technology Landau quantization 021001 nanoscience & nanotechnology 01 natural sciences Density wave theory Condensed Matter - Strongly Correlated Electrons High Energy Physics - Theory (hep-th) Pairing 0103 physical sciences 010306 general physics 0210 nano-technology Spin-½ Fermi Gamma-ray Space Telescope |
| Zdroj: | Physical Review B. 103 |
| ISSN: | 2469-9969 2469-9950 |
| DOI: | 10.1103/physrevb.103.235129 |
| Popis: | We describe the large $N$ saddle point, and the structure of fluctuations about the saddle point, of a theory containing a sharp, critical Fermi surface in two spatial dimensions. The theory describes the onset of Ising order in a Fermi liquid, and closely related theories apply to other cases with critical Fermi surfaces. We employ random couplings in flavor space between the fermions and the bosonic order parameter, but there is no spatial randomness: consequently, the $G$-$\Sigma$ path integral of the theory is expressed in terms of fields bilocal in spacetime. The critical exponents of the large $N$ saddle-point are the same as in the well-studied non-random RPA theory; in particular, the entropy density vanishes in the limit of zero temperature. We present a full numerical solution of the large $N$ saddle-point equations, and the results agree with the critical behavior obtained analytically. Following analyses of Sachdev-Ye-Kitaev models, we describe scaling operators which descend from fermion bilinears around the Fermi surface. This leads to a systematic consideration of the role of time reparameterization symmetry, and the scaling of the Cooper pairing and $2k_F$ operators which can determine associated instabilities of the critical Fermi surface. We find no violations of scaling from time reparameterizations. We also consider the same model but with spatially random couplings: this provides a systematic large $N$ theory of a marginal Fermi liquid with Planckian transport. Comment: 66 pages, 17 figures. v3: discussion improved. published version |
| Databáze: | OpenAIRE |
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