Kondo physics in the algebraic spin liquid

TL;DR

This paper investigates how magnetic impurities behave in an algebraic spin liquid, revealing a quantum phase transition and unique power-law responses influenced by the system's critical properties, with potential experimental implications.

Contribution

It introduces a large-N analysis of impurity behavior in the algebraic spin liquid, uncovering a quantum phase transition and the dependence of Wilson's ratio on critical exponents.

Findings

Identifies a quantum phase transition from local-moment to Kondo-screened phase.

Shows impurity responses follow power-law dependencies due to anomalous exponents.

Proposes Wilson's ratio as a probe for bulk criticality.

Abstract

We study Kondo physics in the algebraic spin liquid, recently proposed to describe $ZnCu_{3}(OH)_{6}Cl_{2}$ [Phys. Rev. Lett. {\bf 98}, 117205 (2007)]. Although spin dynamics of the algebraic spin liquid is described by massless Dirac fermions, this problem differs from the Pseudogap Kondo model, because the bulk physics in the algebraic spin liquid is governed by an interacting fixed point where well-defined quasiparticle excitations are not allowed. Considering an effective bulk model characterized by an anomalous critical exponent, we derive an effective impurity action in the slave-boson context. Performing the large-$N_{\sigma}$ analysis with a spin index $N_{\sigma}$, we find an impurity quantum phase transition from a decoupled local-moment state to a Kondo-screened phase. We evaluate the impurity spin susceptibility and specific heat coefficient at zero temperature, and find that such responses follow power-law dependencies due to the anomalous exponent of the algebraic spin liquid. Our main finding is that the Wilson's ratio for the magnetic impurity depends strongly on the critical exponent in the zero temperature limit. We propose that the Wilson's ratio for the magnetic impurity may be one possible probe to reveal criticality of the bulk system.