Role of non-magnetic disorder on the stability of U(1) spin liquid : A renormalization group study

TL;DR

This study examines how non-magnetic disorder influences the stability of the U(1) spin liquid phase in quantum antiferromagnets, finding stability under weak disorder and localization-induced confinement under strong disorder.

Contribution

It provides a renormalization group analysis of the effects of non-magnetic disorder on the stability of the U(1) spin liquid phase, extending previous work on $QED_3$.

Findings

U1SL remains stable with weak disorder.

Strong disorder leads to localization and confinement.

Deconfinement is suppressed by strong disorder.

Abstract

Recently Hermele et. al claimed that the infrared (IR) fixed point of non-compact $QED_3$ is stable against instanton excitations in the limit of large flavors of massless Dirac fermions [cond-mat/0404751]. We investigate an effect of non-magnetic disorder on the deconfined quantum critical phase dubbed U(1) spin liquid ($U1SL$) in the context of quantum antiferromagnet. In the case of weak disorder the IR fixed point remains stable against the presence of both the instanton excitations and non-magnetic disorder and thus the $U1SL$ is sustained. In the case of strong disorder the IR fixed point becomes unstable against the disorder and the Anderson localization is expected to occur. We argue that in this case deconfinement of spinons does not occur since the Dirac fermion becomes massive owing to the localization.