A method is developed that permits a simple evaluation of two-loop response functions for fermions coupled to a gauge field. We employ this method to study the gauge-invariant response functions in the algebraic Fermi liquid, a non-Fermi liquid state proposed to describe the pseudogap phase in the ${\mathrm{QED}}_{3}$ theory of cuprate superconductors. The staggered spin susceptibility is found to exhibit a characteristic anomalous dimension exponent ${\ensuremath{\eta}}_{4},$ while other correlators show a behavior consistent with the conservation laws imposed by the symmetries of the underlying theory.A method is developed that permits a simple evaluation of two-loop response functions for fermions coupled to a gauge field. We employ this method to study the gauge-invariant response functions in the algebraic Fermi liquid, a non-Fermi liquid state proposed to describe the pseudogap phase in the ${\mathrm{QED}}_{3}$ theory of cuprate superconductors. The staggered spin susceptibility is found to exhibit a characteristic anomalous dimension exponent ${\ensuremath{\eta}}_{4},$ while other correlators show a behavior consistent with the conservation laws imposed by the symmetries of the underlying theory.

arXiv:cond-mat/0211119Physical review. B, Condensed matterJul 18, 200338 citations

Conservation laws and correlation functions in the Luttinger liquid

Walter Metzner, C. Di Castro

The low-energy properties of interacting Fermi systems are highly constrained by conservation laws. They generally simplify the structure of the underlying renormalization group by reducing the number of independent renormalization constants. In one dimension, all properties of normal metallic fixed points are uniquely determined by separate charge and spin conservation for states near the left and right Fermi points, respectively. We construct the general Luttinger-liquid theory of one-dimensional (1D) metals directly from these conservation laws. Luttinger-liquid parameters emerge naturally from the velocities associated with the conserved currents at the Luttinger-liquid fixed point. Instead of bosonization, one may thus use techniques familiar from Fermi-liquid theory, i.e., Feynman diagrams, equations of motion, and Ward identities. The choice of a technique comprising both Fermi- and Luttinger-liquid theory makes the similarities and differences of both theories particularly transparent, and sets the stage for constructing non-Fermi-liquid metallic fixed points in d>1. Several generic properties and asymptotic conservation laws of 2D non-Fermi-liquid metals are discussed.The low-energy properties of interacting Fermi systems are highly constrained by conservation laws. They generally simplify the structure of the underlying renormalization group by reducing the number of independent renormalization constants. In one dimension, all properties of normal metallic fixed points are uniquely determined by separate charge and spin conservation for states near the left and right Fermi points, respectively. We construct the general Luttinger-liquid theory of one-dimensional (1D) metals directly from these conservation laws. Luttinger-liquid parameters emerge naturally from the velocities associated with the conserved currents at the Luttinger-liquid fixed point. Instead of bosonization, one may thus use techniques familiar from Fermi-liquid theory, i.e., Feynman diagrams, equations of motion, and Ward identities. The choice of a technique comprising both Fermi- and Luttinger-liquid theory makes the similarities and differences of both theories particularly transparent, and sets the stage for constructing non-Fermi-liquid metallic fixed points in d>1. Several generic properties and asymptotic conservation laws of 2D non-Fermi-liquid metals are discussed.

Physical review. B, Condensed matterJun 15, 199381 citations

Conditions for l=1 Pomeranchuk instability in a Fermi liquid

Yiming Wu, Avraham Klein, Andrey V. Chubukov

In a Fermi liquid, the stability of the Fermi surface to deformation is encoded in the angular moments of the interaction between quasiparticles via the Pomeranchuk criterion ${F}_{l}$ $\ensuremath{\ge}$ $-1$ . Interestingly, charge and spin conservation prevent interactions from destabilizing the $l$ =1 channel even when ${F}_{l}$ = -1, indicating that high-energy processes play a nontrivial role in the low-energy Fermi liquid dynamics. The authors identify, analytically and numerically, that conservation laws imply an equivalence between processes near and away from the Fermi surface, preventing $l$ =1 instabilities. Then, they construct $l$ =1 order parameters without this equivalence, identifying possible novel instabilities in strongly correlated electron systems.In a Fermi liquid, the stability of the Fermi surface to deformation is encoded in the angular moments of the interaction between quasiparticles via the Pomeranchuk criterion ${F}_{l}$ $\ensuremath{\ge}$ $-1$. Interestingly, charge and spin conservation prevent interactions from destabilizing the $l$=1 channel even when ${F}_{l}$ = -1, indicating that high-energy processes play a nontrivial role in the low-energy Fermi liquid dynamics. The authors identify, analytically and numerically, that conservation laws imply an equivalence between processes near and away from the Fermi surface, preventing $l$=1 instabilities. Then, they construct $l$=1 order parameters without this equivalence, identifying possible novel instabilities in strongly correlated electron systems.

arXiv:1801.06571Physical review. B./Physical review. BApr 2, 201821 citations

{\mathrm{QED}}_{3}

theory of cuprate superconductors. The staggered spin susceptibility is found to exhibit a characteristic anomalous dimension exponent ${\ensuremath{\eta}}_{4},$ while other correlators show a behavior consistent with the conservation laws imposed by the symmetries of the underlying theory.

In a Fermi liquid, the stability of the Fermi surface to deformation is encoded in the angular moments of the interaction between quasiparticles via the Pomeranchuk criterion

{F}_{l}

$\ensuremath{\ge}$

-1

. Interestingly, charge and spin conservation prevent interactions from destabilizing the

l

=1 channel even when

{F}_{l}

= -1, indicating that high-energy processes play a nontrivial role in the low-energy Fermi liquid dynamics. The authors identify, analytically and numerically, that conservation laws imply an equivalence between processes near and away from the Fermi surface, preventing

l

=1 instabilities. Then, they construct

l

=1 order parameters without this equivalence, identifying possible novel instabilities in strongly correlated electron systems.