From four- to two-channel Kondo effect in junctions of XY spin chains

Abstract

We consider the Kondo effect in Y-junctions of anisotropic XY models in an applied magnetic field along the critical lines characterized by a gapless excitation spectrum. We find that, while the boundary interaction Hamiltonian describing the junction can be recasted in the form of a four-channel, spin-1/2 antiferromagnetic Kondo Hamiltonian, the number of channels effectively participating in the Kondo effect depends on the chain parameters, as well as on the boundary couplings at the junction. The system evolves from an effective four-channel topological Kondo effect for a junction of XX-chains with symmetric boundary couplings into a two-channel one at a junction of three quantum critical Ising chains. The effective number of Kondo channels depends on the properties of the boundary and of the bulk. The XX-line is a "critical" line, where a fourchannel topological Kondo effect can be recovered by fine-tuning the boundary parameter, while along the line in parameter space connecting the XX-line and the critical Ising point the junction is effectively equivalent to a two-channel topological Kondo Hamiltonian. Using a renormalization group approach, we determine the flow of the boundary couplings, which allows us to define and estimate the critical couplings and Kondo temperatures of the different Kondo (pair) channels. Finally, we study the local transverse magnetization in the center of the Y-junction, eventually arguing that it provides an effective tool to monitor the onset of the two-channel Kondo effect.

Two-channel Kondo physics in a Majorana island coupled to a Josephson junction

“…A related destabilization of the SO(M ) 2 fixed point was recently reported for M = 3 (corresponding to a crossover from 4-channel to 2CK states) in a related spin chain context in Ref. 32 As is well known, multichannel Kondo effects are destabilized by channel anisotropy; however, while in topological Kondo setups lead-anisotropy remarkably does not yield any channel anisotropy, we see that the Josephson coupling does lead to channel anisotropy at the topological Kondo fixed point, which is hence unstable. We may start drawing the charging dominated side of the phase diagram of the device, see Fig.…”

Universal scaling for the quantum Ising chain with a classical impurity

“…Therefore, while we plan to address in detail this issue in a forthcoming publication, here we limit ourselves to a few additional observations on the two-length generalized scaling formula in Eq. (27). First of all, we note that, as μ → 1 (that FIG.…”

“…Typically, the impurity dynamics affects bulk quantities (such as the conductance, or the spin susceptibility), and, in turn, it can be probed by looking at the bulk response through suitably designed devices. Recently, impurity-induced dynamics has been investigated, e.g., in Josephson junction networks [20][21][22][23], quantum spin chains [24][25][26][27][28][29], and cold fermion gases [30][31][32][33].…”

Kondo length in bosonic lattices

“…Eq. (27) illustrates how the function we explicitly use in our calculation can be regarded as just an approximation to the exact scaling function for Σ z (x). A more refined analytical treatment might in principle be done by considering higher-order contributions in perturbation theory in S B G .…”