Two Channel Kondo behavior in the quantum XX chain with a boundary defect

TL;DR

This paper shows that a boundary defect in the quantum XX chain exhibits two-channel Kondo physics, with fractionalization into Majorana fermions and unique boundary behaviors, including a non-integer g-function value.

Contribution

It reveals the realization of two-channel Kondo physics in a quantum XX chain with a boundary defect, including Majorana fermion fractionalization and boundary-bound modes.

Findings

Edge spin fractionalizes into two Majorana fermions.

The g-function reaches a non-integer value of √2.

Boundary-bound mode becomes localized for strong impurity coupling.

Abstract

We demonstrate that a boundary defect in the single spin-$\frac{1}{2}$ quantum $XX$ chain exhibits two-channel Kondo physics. Due to the presence of the defect, the edge spin fractionalizes into two Majorana fermions, out of which one decouples, and one is overscreened by the free fermion in bulk, leading to non-trivial boundary behavior characteristic of the two-channel Kondo model. When the ratio of boundary to bulk coupling exceeds a critical value of $\sqrt{2}$, a massive boundary-bound mode is exponentially localized near the impurity site for strong impurity coupling. This leads to unusual behavior in physical quantities, such as the $g$-function not being monotonic. We compute the $g-$function of the impurity from both thermodynamic and entanglement entropy calculations and show that it takes a non-integer value of $\sqrt{2}$ just as in the two-channel Kondo problem.