# Entanglement entropy and boundary renormalization group flow - exact results in the Ising universality class

## TL;DR

This paper provides exact conformal field theory calculations of boundary entanglement entropy in the Ising universality class, illustrating universal boundary RG flow consistent with the g-theorem and applicable to related quantum critical models.

## Contribution

It introduces an exact analytical expression for boundary entanglement entropy in the Ising class using bosonization of twist fields, extending understanding of boundary RG flows and universality.

## Key findings

- Exact boundary entanglement entropy formula derived
- Universal boundary RG flow consistent with g-theorem demonstrated
- Application to quantum critical models like the two-channel Kondo model

## Abstract

The entanglement entropy in one dimensional critical systems with boundaries has been associated with the noninteger ground state degeneracy. This quantity, being a characteristic of boundary fixed points, decreases under renormalization group flow, as predicted by the g-theorem. Here, using conformal field theory methods, we exactly calculate the entanglement entropy in the boundary Ising universality class. Our expression can be separated into the well known bulk term and a boundary entanglement term, displaying a universal flow between two boundary conditions, in accordance with the g-theorem. These results are obtained within the replica trick approach, where we show that the associated twist field, a central object generating the geometry of an $n$-sheeted Riemann surface, can be bosonized, giving simple analytic access to multiple quantities of interest. We argue that our result applies to other models falling into the same universality class. This includes the vicinity of the quantum critical point of the two-channel Kondo model, allowing to track in real space the presence of a region containing one half of a qubit with entropy $\frac{1}{2} \log (2)$, associated with a free local Majorana fermion.