Quantum phase transitions of metals in two spatial dimensions: I. Ising-nematic order

By M. Metlitski, S. Sachdev. 2010

301 citations recorded by the source corpus.

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 2+1 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 by 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.

Subfields: Condensed Matter Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/ecd5f1ae2470397964be6eb56fece6bb251d2d3c

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Citations in the corpus

Functional renormalization group approach to correlated fermion systems (2011, methodology): “The Hertz-Millis approach was also shown to be invalid for the quantum antiferromagnetic transition in two dimensions (Abanov and Chubukov, 2004; Abanov et al., 2003; Metlitski and Sachdev, 2010a).”
Hidden Fermi surfaces in compressible states of gauge-gravity duality (2011, methodology): “[53], the symbol z was used for the dynamic scaling of a boson Green’s function).”
Electron stars for holographic metallic criticality (2010, unknown): “It has recently been demonstrated [5, 6, 4] that the vector large N expansion breaks down for 2+1 dimensional metallic quantum critical systems.”
What Can Gauge-Gravity Duality Teach Us about Condensed Matter Physics? (2011, background): “The parameters η and z are critical exponents whose values can be estimated in various expansion methods [40, 41].”