Abstract
We present a renormalization-group theory for the onset of Ising-nematic order in a Fermi liquid in two spatial dimensions. This is a quantum phase transition, driven by electron interactions, which spontaneously reduces the point-group symmetry from square to rectangular. The critical point is described by an infinite set of -dimensional local field theories, labeled by points on the Fermi surface. Each field theory contains a real scalar field representing the Ising order parameter and fermionic fields representing a time-reversed pair of patches on the Fermi surface. We demonstrate that the field theories obey compatibility constraints required by our redundant representation of the underlying degrees of freedom. Scaling forms for the response functions are proposed and supported by computations up to three loops. Extensions of our results to other transitions of two-dimensional Fermi liquids with broken point-group and/or time-reversal symmetry are noted. Our results extend also to the problem of a Fermi surface coupled to a U(1) gauge field.
4 More- Received 28 February 2010
DOI:https://doi.org/10.1103/PhysRevB.82.075127
©2010 American Physical Society
Viewpoint
Hidden one-dimensional physics in 2D critical metals
Published 16 August 2010
New theoretical work shows that in two-dimensional condensed matter systems, one-dimensional processes such as forward or backward scattering have a dramatic effect on the physical behavior of fermions near a quantum critical point and derail attempts to get an accurate description of a non-Fermi-liquid.
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