Critical particle-hole composites at twice the Fermi wave vector in U(1) spin liquid with a Fermi surface

TL;DR

This paper explores critical particle-hole composite states at twice the Fermi momentum in a U(1) spin liquid, revealing chiral symmetry breaking and analyzing the effects using a Nambu-Eliashberg framework with implications for thermodynamics.

Contribution

It introduces a Nambu-Eliashberg theoretical approach to analyze particle-hole composites and chiral symmetry breaking in U(1) spin liquids with a Fermi surface, highlighting novel quantum corrections.

Findings

Identification of chiral symmetry breaking at finite energies.

Derivation of pairing self-energy with power law frequency dependence.

Thermodynamics governed by z=3 scaling free energy unaffected by pairing corrections.

Abstract

We find "{\it chiral symmetry breaking}" at finite energies in U(1) spin liquid, corresponding to critical particle-hole composite states with twice of the Fermi momentum (2$k_{F}$). We investigate this Fermi surface problem based on the Nambu-Eliashberg theory, where the off diagonal pairing self-energy is introduced to catch the Aslamasov-Larkin vertex correction. This approach is quite parallel with the case of superconductivity, where such Aslamasov-Larkin quantum corrections in the particle-particle channel are well known to be responsible for superconducting instability, formulated as the Nambu-Eliashberg theory in an elegant way. We obtain the pairing self-energy, which vanishes at zero energy but displays the same power law dependence for frequency as the normal Eliashberg self-energy. As a result, even the pairing self-energy correction does not modify the Eliashberg dynamics without the Nambu spinor representation, where thermodynamics is described by the typical $z = 3$ scaling free energy. We discuss physical implication of the anomalous self-energy identical to the conventional Eliashberg normal self-energy, focusing on thermodynamics.