Long-range entanglement near a Kondo-destruction quantum critical point

TL;DR

This study uses numerical renormalization group methods to analyze quantum entanglement near a Kondo-destruction quantum critical point, revealing a universal entanglement length scale that diverges at criticality.

Contribution

It introduces a detailed analysis of entanglement entropy and length scale behavior near the Kondo-destruction quantum critical point using NRG.

Findings

Identification of a characteristic entanglement length scale R*

Universal scaling of entanglement entropy with R/R*

R* diverges at the quantum critical point with a r-dependent exponent

Abstract

The numerical renormalization group is used to study quantum entanglement in the Kondo impurity model with a pseudogapped density of states $\rho(\varepsilon)\propto|\varepsilon|^r$ ($r>0$) that vanishes at the Fermi energy $\varepsilon=0$. The model features a Kondo-destruction quantum critical point (QCP) separating a partially screened phase (reached for impurity-band exchange couplings $J>J_c$) from a local-moment phase ($J<J_c$). The impurity contribution $S_e^{imp}$ to the entanglement entropy between a region of radius $R$ around the magnetic impurity and the rest of the host system reveals a characteristic length scale $R^*$ that distinguishes a regime $R\ll R^*$ of maximal critical entanglement from one $R\gg R^*$ of weaker entanglement. Within each phase, $S_e^{imp}$ is a universal function of $R/R^*$ with a power-law decay for $R/R^*\gg 1$. The entanglement length scale $R^*$ diverges on approach to the QCP with a critical exponent that depends only on $r$.