Effect of nonmagnetic disorder on criticality in the "dirty" U(1) spin liquid

TL;DR

This paper studies how nonmagnetic disorder affects the stability of the algebraic spin liquid (ASL) using an effective field theory, revealing that the critical exponent determines whether the ASL remains stable or localizes, with implications for high-temperature cuprates.

Contribution

It introduces an effective nonlinear sigma model approach to analyze the impact of disorder on the ASL's criticality, highlighting the role of the anomalous critical exponent.

Findings

Positive critical exponent leads to unstable fixed point and delocalization.

Negative exponent causes Anderson localization of the ASL.

Power law suppression of spinon density of states observed.

Abstract

We investigate the effect of nonmagnetic disorder on the stability of the algebraic spin liquid ($ASL$) by deriving an effective field theory, nonlinear $\sigma$ model ($NL{\sigma}M$). We find that the anomalous critical exponent characterizing the criticality of the $ASL$ causes an anomalous gradient in the $NL{\sigma}M$. We show that the sign of the anomalous gradient exponent or the critical exponent of the $ASL$ determines the stability of the "dirty" $ASL$. A positive exponent results in an unstable fixed point separating delocalized and localized phases, which is consistent with our previous study [Phys. Rev. B {\bf 70}, 140405 (2004)]. We find power law suppression for the density of spinon states in contrast to the logarithmic correction in the free Dirac theory. On the other hand, a negative exponent destabilizes the $ASL$, causing the Anderson localization. We discuss the implication of our study in the pseudogap phase of high $T_c$ cuprates.