Integrable versus Non-Integrable Spin Chain Impurity Models

TL;DR

This paper investigates the differences between integrable and non-integrable impurity models in spin-1/2 chains, clarifying their phase diagrams and renormalization group flows near the integrable point.

Contribution

It provides a detailed analysis of the integrable impurity model, showing it corresponds to a multi-critical point and reconciling previous RG and Bethe ansatz results.

Findings

The integrable impurity model is a multi-critical point.

A consistent RG flow and phase diagram are proposed.

The study clarifies discrepancies between RG and Bethe ansatz results.

Abstract

Recent renormalization group studies of impurities in spin-1/2 chains appear to be inconsistent with Bethe ansatz results for a special integrable model. We study this system in more detail around the integrable point in parameter space and argue that this integrable impurity model corresponds to a non-generic multi-critical point. Using previous results on impurities in half-integer spin chains, a consistent renormalization group flow and phase diagram is proposed.