Macroscopic Quantum Entanglement of a Kondo Cloud at Finite Temperature

Abstract

We propose a variational approach for computing the macroscopic entanglement in a many-body mixed state, based on entanglement witness operators, and compute the entanglement of formation (EoF), a mixed-state generalization of the entanglement entropy, in single- and two-channel Kondo systems at finite temperature. The thermal suppression of the EoF obeys power-law scaling at low temperature. The scaling exponent is halved from the single- to the two-channel system, which is attributed, using a bosonization method, to the non-Fermi liquid behavior of a Majorana fermion, a "half" of a complex fermion, emerging in the two-channel system. Moreover, the EoF characterizes the size and power-law tail of the Kondo screening cloud of the single-channel system.

Supplementary Material included

References in corpus (12)

• Entanglement detection
• The numerical renormalization group method for quantum impurity systems
• Entanglement negativity in quantum field theory
• Sum-rule Conserving Spectral Functions from the Numerical Renormalization Group
• Quantifying Entanglement with Witness Operators
• Kondo screening cloud in a one dimensional wire: Numerical renormalization group study
• Thermal bound entanglement in macroscopic systems and area laws
• Impurity entanglement entropy in Kondo systems from conformal field theory
• Construction of optimal witness for unknown two-qubit entanglement
• Entanglement of an impurity and conduction spins in the Kondo model
• Minimax optimization of entanglement witness operator for the quantification of three-qubit mixed-state entanglement
• Quantifying mixed-state quantum entanglement by optimal entanglement witness

Cited by in corpus (11)

• Thermometry of Strongly Correlated Fermionic Quantum Systems using Impurity Probes
• The fate of the Kondo cloud in a superconductor
• Realistic protocol to measure entanglement at finite temperatures
• Universal Thermal Entanglement of Multichannel Kondo Effects
• Entanglement based observables for quantum impurities
• Hierarchical entanglement shells of multichannel Kondo clouds
• Unveiling the Kondo cloud: unitary RG study of the Kondo model
• Non-Hermitian Numerical Renormalization Group: Solution of the non-Hermitian Kondo model
• System-bath entanglement of noninteracting fermionic impurities: Equilibrium, transient, and steady-state regimes
• Long-range Entanglement of Kondo Clouds in Open Triple Quantum Dots
• Kondo Screening Cloud Scaling: Impurity Entanglement and Magnetization