Abstract
We describe the large- 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 path integral of the theory is expressed in terms of fields bilocal in spacetime. The critical exponents of the large- saddle point are the same as in the well-studied nonrandom random-phase-approximation theory; in particular, the entropy density vanishes in the limit of zero temperature. We present a full numerical solution of the large- 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 reparametrization symmetry, and the scaling of the Cooper pairing and operators which can determine associated instabilities of the critical Fermi surface. We find no violations of scaling from time reparametrizations. We also consider the same model but with spatially random couplings: this provides a systematic large- theory of a marginal Fermi liquid with Planckian transport.
10 More- Received 22 March 2021
- Accepted 25 April 2021
DOI:https://doi.org/10.1103/PhysRevB.103.235129
©2021 American Physical Society
Physics Subject Headings (PhySH)
Viewpoint
When the Disorder is Just Right
Published 14 June 2021
A new model suggests that disorder can be a crucial ingredient for producing non-Fermi-liquid behavior in a system of interacting fermions.
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