Kondo length in bosonic lattices

Abstract

Motivated by the fact that the low-energy properties of the Kondo model can be effectively simulated in spin chains, we study the realization of the effect with bond impurities in ultracold bosonic lattices at half-filling. After presenting a discussion of the effective theory and of the mapping of the bosonic chain onto a lattice spin Hamiltonian, we provide estimates for the Kondo length as a function of the parameters of the bosonic model. We point out that the Kondo length can be extracted from the integrated real space correlation functions, which are experimentally accessible quantities in experiments with cold atoms.

From Kondo effect to weak-link regime in quantum spin- 12 spin chains

“…To conclude this section, it is worth stressing the important point about H, addressed in detail in appendix A, that, besides describing a single spin in a generically nonzero magnetic field weakly coupled to two uniform spin chains, it can be regarded as an effective description of a generic few-spin spin cluster (an "extended region") in the middle of an otherwise uniform chain, weakly coupled to the rest of the chains at its endpoints. An extended region is closer to what one expects to realize in a bosonic cold-atom lattice 30 . In such systems, one can in general simulate quantum spin models by loading the quantum gas(es) on optical lattices 43 .…”

“…The fact that one cannot perfectly center these additional potentials exactly between two lattice sites finally results in an asymmetry of the couplings (see Ref. [30]), such as the one we discuss here. However, generically the added potentials will have a width σ larger than one or two lattice sites spacing.…”

“…The derivation of the finite-τ correlation functions G +,− (x, x ′ ; τ |ℓ) = T τ S + x (τ )S − x ′ (0) and G z,z (x, x ′ ; τ |ℓ) = T τ S z x (τ )S z x ′ (0) , is discussed in detail in Ref. [30]. Here, we just quote the main result, which we have diffusely used in the body of our paper.…”

“…(C3) reduce back to the ones implemented in Ref. [30] to derive the Kondo screening length in various regimes. In that case, it is possible to provide a closed-form solution for the integral curves, from which one can extract the analytical expression of ξ K .…”

Tunable spin/charge Kondo effect at a double superconducting island connected to two spinless quantum wires

“…Recently, a renewed interest has arisen in the Kondo effect 7 , due to the possibility of realizing it in a controlled way in mesoscopic systems with tunable parameters, such as semiconducting quantum dots with metallic leads [8][9][10][11] , in which Kondo effect is expected to appear in an upturn of the conductance, rather than of the resistivity, across the dot connected to the leads, or with superconducting leads [12][13][14] , in which Kondo effect should be evidenced by a change in the behavior of the subgap (Josephson) supercurrent across the dot, when the leads are held at a fixed phase difference ϕ. In addition, since the effect is merely due to spin dynamics, it has been proposed that a "spin-Kondo" effect can take place in systems with itinerant, low-energy excitations carrying spin, but not charge, such as XXZ spin-1/2 chains [15][16][17] , which can be for instance realized by loading cold atoms on a pertinently designed optical lattice 18,19 , or frustrated J 1 − J 2 spin chains with J 2 /J 1 tuned at the "critical" value at the phase transition between the spin liquid-and the dimerized-phase of the system 20 . In fact, a tunable realization of the spin-Kondo effect has recently been proposed at junctions of quantum spin chains [21][22][23][24] , or of one-dimensional arrays of Josephson junctions [25][26][27] .…”