Kondo effect in XXZ spin chains

Abstract

The Kondo effect in a one-dimensional spin-1/2 XXZ model in the gapless XY regime (-1<Delta<=1) is studied both analytically and numerically. In our model an impurity spin (S=1/2) is coupled to a single spin in the XXZ spin chain. Perturbative renormalization-group (RG) analysis is performed for various limiting cases to deduce low-energy fixed points. It is shown that in the ground state the impurity spin is screened by forming a singlet with a spin in the host XXZ chain. In the antiferromagnetic side (0<Delta<=1) the host chain is cut into two semi-infinite chains by the singlet. In the ferromagnetic side (-1<Delta<0), on the other hand, the host XXZ chain remains as a single chain through "healing" of a weakened bond in the low-energy (long-distance) limit. The density matrix renormalization group method is used to study the size scaling of finite-size energy gaps and the power-law decay of correlation functions in the ground state. The numerical results are in good agreement with the predictions of the RG analysis. Low-temperature behaviors of specific heat and susceptibility are also discussed.

11 pages including 12 Postscript figures

References in corpus (6)

• Exact Results for a Kondo Problem in One Dimensional t-J Model
• Impurity in a Luttinger liquid away from half-filling: a numerical study
• Edge Magnetic Field in the xxz Spin-1/2 Chain
• Scaling and criticality of the Kondo effect in a Luttinger liquid
• Low-temperature behavior of a Magnetic Impurity in a Heisenberg Chain
• Multichannel Kondo Effect in an Interacting Electron System: Exact Results for the Low-Temperature Thermodynamics

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• Tunable spin/charge Kondo effect at a double superconducting island connected to two spinless quantum wires
• Thermal transport in a spin-1/2 Heisenberg chain coupled to a (non) magnetic impurity
• Universal scaling of a classical impurity in the quantum Ising chain
• From Kondo effect to weak-link regime in quantum spin-1/2 spin chains
• Crossover of Correlation Functions near a Quantum Impurity in a Tomonaga-Luttinger Liquid
• Edge modes and boundary impurities in the anisotropic Heisenberg spin chain
• Quantum Zeno Effect in Noisy Integrable Quantum Circuits for Impurity Models
• Kondo Length in Bosonic Lattices
• Transport properties of a spin-1/2 Heisenberg chain with an embedded spin-S impurity
• Nano-welding of quantum spin-$1/2$ chains at minimal dissipation
• Tunneling spectroscopy of the spinon-Kondo effect in one-dimensional Mott insulators