Natural Orbitals Renormalization Group Approach to the Two-Impurity Kondo Critical Point

Abstract

The problem of two magnetic impurities in a normal metal exposes the two opposite tendencies in the formation of a singlet ground state, driven respectively by the single-ion Kondo effect with conduction electrons to screen impurity spins or the Ruderman-Kittel-Kasuya-Yosida interaction between the two impurities to directly form impurity spin singlet. However, whether the competition between these two tendencies can lead to a quantum critical point has been debated over more than two decades. Here, we study this problem by applying the newly proposed natural orbitals renormalization group method to a lattice version of the two-impurity Kondo model with a direct exchange $K$ between the two impurity spins. The method allows for unbiased accessing the ground state wave functions and low-lying excitations for sufficiently large system sizes. We demonstrate the existence of a quantum critical point, characterized by the power-law divergence of impurity staggered susceptibility with critical exponent $\gamma =0.60(1)$, on the antiferromagnetic side of $K$ when the interimpurity distance $R$ is even lattice spacing, while a crossover behavior is recovered when $R$ is odd lattice spacing. These results have ultimately resolved the long-standing discrepancy between the numerical renormalization group and quantum Monte Carlo studies, confirming a link of this two-impurity Kondo critical point to a hidden particle-hole symmetry predicted by the local Fermi liquid theory.

10 pages, 12 figures

References in corpus (6)

• Quantum Criticality in Heavy Fermion Metals
• Quantum criticality in a double quantum-dot system
• Interplay between Kondo effect and Ruderman-Kittel-Kasuya-Yosida interaction
• An order parameter for impurity systems at quantum criticality
• Kondo versus indirect exchange: the role of the lattice and the actual range of RKKY interactions in real materials
• Coherence scale of coupled Anderson impurities

Cited by in corpus (6)

• $\text{Ab initio}$ dynamical mean-field theory with natural orbitals renormalization group impurity solver: Formalism and applications
• Order parameter for the multichannel Kondo model at quantum criticality
• Magnetic correlation between two local spins in a quantum spin Hall insulator
• Natural orbitals renormalization group approach to a spin-1/2 impurity interacting with two helical liquids
• Infinite Grassmann time-evolving matrix product operators for quantum impurity problems after a quench
• Scalable tensor network algorithm for quantum impurity problems