Entanglement structure of the two-channel Kondo model

Abstract

Two electronic channels competing to screen a single impurity spin, as in the two-channel Kondo model, are expected to generate a ground state with nontrivial entanglement structure. We exploit a spin-chain representation of the two-channel Kondo model to probe the ground-state block entropy, negativity, tangle, and Schmidt gap, using a density matrix renormalization group approach. In the presence of symmetric coupling to the two channels we confirm field-theory predictions for the boundary entropy difference, $\ln (g_{UV}/g_{IR})=\ln (2)/2$, between the ultraviolet and infrared limits and the leading $\ln (x)/x$ impurity correction to the block entropy. The impurity entanglement, $S_{\text{imp}}$, is shown to scale with the characteristic length ${\xi }_{2CK}$. We show that both the Schmidt gap and the entanglement of the impurity with one of the channels $-$ as measured by the negativity$-$ faithfully serve as order parameters for the impurity quantum phase transition appearing as a function of channel asymmetry, allowing for explicit determination of critical exponents, $\nu \approx 2$ and $\beta \approx 0.2$. Remarkably, we find the emergence of tripartite entanglement only in the vicinity of the critical channel-symmetric point.

5 pages + 2 pages of supplemental material

References in corpus (13)

• Observation of the two-channel Kondo effect
• Monogamy Inequality in terms of Negativity for Three-Qubit States
• Two-channel Kondo effect and renormalization flow with macroscopic quantum charge states
• Universal Fermi liquid crossover and quantum criticality in a mesoscopic device
• Entanglement and Criticality in Quantum Impurity Systems
• An order parameter for impurity systems at quantum criticality
• Universal and measurable entanglement entropy in the spin-boson model
• Universal low-temperature crossover in two-channel Kondo models
• Impurity Entanglement Entropy and the Kondo Screening Cloud
• Macroscopic Quantum Entanglement of a Kondo Cloud at Finite Temperature
• Kondo Effect in Spin Chains
• Impurity entanglement entropy in Kondo systems from conformal field theory
• Dynamical correlations in the spin-half two-channel Kondo model

Cited by in corpus (38)

• Quantum entanglement in condensed matter systems
• The g-theorem and quantum information theory
• Machine Learning Assisted Many-Body Entanglement Measurement
• The entanglement negativity in random spin chains
• Negativity spectrum of one-dimensional conformal field theories
• Quantum information dynamics in multipartite integrable systems
• Entanglement spectrum degeneracy and Cardy formula in 1+1 dimensional conformal field theories
• Spin structures and entanglement of two disjoint intervals in conformal field theories
• Entanglement negativity in a two dimensional harmonic lattice: Area law and corner contributions
• Scaling of tripartite entanglement at impurity quantum phase transitions
• Negativity spectrum in 1D gapped phases of matter
• From four- to two-channel Kondo effect in junctions of XY spin chains
• Entanglement and classical fluctuations at finite-temperature critical points
• Entanglement entropy and negativity in the Ising model with defects
• Information scrambling at an impurity quantum critical point
• Universal Thermal Entanglement of Multichannel Kondo Effects
• Entanglement entropy after selective measurements in quantum chains
• Chiral Y junction of quantum spin chains
• Numerical renormalization group method for entanglement negativity at finite temperature
• Entanglement entropy and boundary renormalization group flow - exact results in the Ising universality class
• Junction of three off-critical quantum Ising chains and two-channel Kondo effect in a superconductor
• Quantum spin circulator in Y junctions of Heisenberg chains
• Hierarchical entanglement shells of multichannel Kondo clouds
• Long-range multipartite quantum correlations and factorization in a one-dimensional spin-1/2 $XY$ chain
• Quantum impurity models using superpositions of fermionic Gaussian states: Practical methods and applications
• Scale Invariant Entanglement Negativity at the Many-Body Localization Transition
• Amplified multipartite entanglement witnessed in a quantum critical metal
• SU(4) Kondo entanglement in double quantum dot devices
• Valence bond fluctuations in the Kitaev spin model
• Cavity-enhanced Kondo effect
• Direct Entropy Measurement in a Mesoscopic Quantum System
• Order parameter for the multichannel Kondo model at quantum criticality
• System-bath entanglement of noninteracting fermionic impurities: Equilibrium, transient, and steady-state regimes
• Frustration shapes multi-channel Kondo physics: a star graph perspective
• Quasiparticle mass enhancement as a measure of entanglement in the Kondo problem
• Two Channel Kondo behavior in the quantum XX chain with a boundary defect
• Ballistic Entanglement Cloud after a Boundary Quench
• Kondo Screening Cloud Scaling: Impurity Entanglement and Magnetization