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

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.

5 pages, 4 Figures

References in corpus (33)

• Unpaired Majorana fermions in quantum wires
• The numerical renormalization group method for quantum impurity systems
• The ITensor Software Library for Tensor Network Calculations
• Fractons
• Topological Defect Lines and Renormalization Group Flows in Two Dimensions
• Boundary effects in the critical scaling of entanglement entropy in 1D systems
• On the Boundary Entropy of One-dimensional Quantum Systems at Low Temperature
• Conformal Field Theory Approach to the 2-Impurity Kondo Problem: Comparison with Numerical Renormalization Group Results
• Wrinkling hierarchy in constrained thin sheets from suspended graphene to curtains
• Two-channel Kondo effect and renormalization flow with macroscopic quantum charge states
• Entanglement entropy in quantum impurity systems and systems with boundaries
• Quantum Dimension as Entanglement Entropy in 2D CFTs
• The g-theorem and quantum information theory
• Tunable Quantum Criticality and Super-ballistic Transport in a `Charge' Kondo Circuit
• Pedestrian Approach to the Two-Channel Kondo Model
• Multi-channel Kondo impurity dynamics in a Majorana device
• Fractional entropy of multichannel Kondo systems from conductance-charge relations
• Solution of the Multichannel Coqblin-Schrieffer Impurity Model and Application to Multi-Level systems
• Universal low-temperature crossover in two-channel Kondo models
• Generic optical excitations of correlated systems: $\pi$-tons
• Quantum simulation of an exotic quantum critical point in a two-site charge Kondo circuit
• Exact solution of the open Heisenberg chain with two impurities
• Anyons in Multichannel Kondo Systems
• Entanglement structure of the two-channel Kondo model
• Kondo Effect in Spin Chains
• On O(1) contributions to the free energy in Bethe Ansatz systems: the exact g-function
• Possibility of direct observation of edge Majorana modes in quantum chains
• Quantum dimensions from local operator excitations in the Ising model
• Kondo effect in the isotropic Heisenberg spin chain
• Low-temperature behavior of a Magnetic Impurity in a Heisenberg Chain
• From Kondo effect to weak-link regime in quantum spin-1/2 spin chains
• Quantum Zeno Effect in Noisy Integrable Quantum Circuits for Impurity Models
• The Kondo effect in the quantum $XX$ spin chain

Cited by in corpus (1)

• Edge States Effects in Quantum Work Statistics