Fermionization for charge degrees of freedom and bosonization of spin degrees of freedom in the SU(2) slave-boson theory

TL;DR

This paper develops an effective field theory combining fermionized charge and bosonized spin in the SU(2) slave-boson framework, revealing non-Fermi liquid behavior and potential instabilities in doped antiferromagnets.

Contribution

It introduces a novel combined fermion-boson effective field theory for charge and spin in the SU(2) slave-boson model, linking valence bond fluctuations with hole dynamics.

Findings

Demonstrates hole deconfinement near quantum critical points.

Finds non-Fermi liquid thermodynamics and transport with z=3 criticality.

Discusses possible superconducting and density wave instabilities.

Abstract

Fermionizing the charge sector and bosonizing the spin part in the SU(2) slave-boson theory, we derive an effective field theory for dynamics of doped holes in the antiferromagnetically correlated spin background, where spin fluctuations are described by an SO(5) Wess-Zumino-Witten (WZW) theory while dynamics of doped holes is characterized by QED$_{3}$ with a chemical potential term. An important feature of our effective field theory is the coupling term between valance bond fluctuations and doped holes. Considering that valance bond fluctuations are deeply related with monopole excitations of staggered U(1) gauge fields in the bosonic field theory for spin fluctuations, we demonstrate that hole dynamics helps deconfinement of bosonic spinons near the quantum critical point of the SO(5) WZW theory. We solve this effective field theory in the Eliashberg framework, and find non-Fermi liquid physics in thermodynamics and transport, where $z = 3$ criticality with dynamical exponent $z$ plays an important role for hole dynamics. We discuss validity of our field theory, applying it to a doped spin chain and comparing it with the slave-fermion framework. Furthermore, we discuss instability of the anomalous metallic phase against superconductivity and density waves of doped holes, resulting from competition between gauge and valance bond fluctuations.