Entanglement and Criticality in Quantum Impurity Systems

TL;DR

This paper explores how entanglement between a spin and its environment peaks at quantum phase transitions in impurity systems, using the spin-boson model and numerical methods to reveal critical behavior.

Contribution

It establishes a link between quantum criticality and impurity entanglement entropy, demonstrating a maximum at phase transitions using the spin-boson model and numerical renormalization.

Findings

Entanglement entropy peaks at quantum critical points.

A cusp in entanglement entropy indicates a phase transition.

Criticality correlates with maximum impurity entanglement.

Abstract

We investigate the entanglement between a spin and its environment in impurity systems which exhibit a second-order quantum phase transition. As an application, we employ the spin-boson model, describing a two-level system (spin) coupled to a subohmic bosonic bath with power-law spectral density, ${\cal J}(\omega)\propto \omega^s$ and $0<s<1$. Combining Wilson's Numerical Renormalization Group method and hyperscaling relations, we demonstrate that the entanglement between the spin and its environment is always enhanced at the quantum phase transition resulting in a visible cusp (maximum) in the entropy of entanglement. We formulate a correspondence between criticality and impurity entanglement entropy, and the relevance of these ideas to Nano-systems is outlined.