Spin-1 two-impurity Kondo problem on a lattice

Abstract

We present an extensive study of the two-impurity Kondo problem for spin-1 adatoms on square lattice using an exact canonical transformation to map the problem onto an effective one-dimensional system that can be numerically solved using the density matrix renormalization group method. We provide a simple intuitive picture and identify the different regimes, depending on the distance between the two impurities, Kondo coupling JK , longitudinal anisotropy D, and transverse anisotropy E. In the isotropic case, two impurities on opposite(same) sublattices have a singlet(triplet) ground state. However, the energy difference between the triplet ground state and the singlet excited state is very small and we expect an effectively four-fold degenerate ground state, i.e., two decoupled impurities. For large enough JK the impurities are practically uncorrelated forming two independent underscreened states with the conduction electrons, a clear non-perturbative effect. When the impurities are entangled in an RKKY-like state, Kondo correlations persists and the two effects coexist: the impurities are underscreened, and the dangling spin-1/2 degrees of freedom are responsible for the inter-impurity entanglement. We analyze the effects of magnetic anisotropy in the development of quasi-classical correlations.

Equilibrium and real-time properties of the spin correlation function in the two-impurity Kondo model

“…Furthermore, one should note that when the distance approaches the Kondo length scale, R ∼ ξ K , large J and R in Fig. 2(a), the Kondo effect leads to a drastic departure from the conventional RKKY interaction [51]. While for small J and R the position of the sign change of the RKKY interaction agrees with the position of the sign change of the correlation function, the latter is shifted towards the integer distances k F R/π = n with increasing coupling J and distance R. The interval in the vicinity of the distances k F R/π = n where we observe ferromagnetic correlation, therefore, shrinks and antiferromagnetic correlations between the impurity spins emerge instead [22].…”

A Numerically Exact Approach to Quantum Impurity Problems in Realistic Lattice Geometries

“…Although briefly suggested in Büsser et al [27], the block Lanczos method was formally introduced in Shirakawa and Yunoki [29] to study spin-spin correlations between an impurity and conduction electrons in graphene. The folding transformation was later used to investigate the competition between Kondo and RKKY physics on different geometries with small [28] and large spin [81] and a number of surprising results were found. Notably, there are important non-perturbative effects that in some cases make Kondo more robust than an RKKY state, even at short distances [28] of the order of a few lattice sites.…”

“…Moreover, due to the fast decay of the RKKY interaction, Kondo screening becomes the dominant effect at relatively short inter-impurity separation. Interestingly, in the spin-1 problem, it was found that impurities can be practically screened by the substrate, while simultaneously forming an RKKY state [81].…”

Effective spin-2 quasi-particles at linear dispersive five-fold degenerate points with tunable topological Chern numbers

“…These have distinct topological properties [32][33][34]. In addition to the works mentioned above, spin-1 can also be realized in condensed matter systems [35][36][37][38][39], quantum systems [40][41][42], and cold atom or lattice models [43][44][45][46][47][48][49]. As for spin-3/2, the massive relativistic spin-3/2 quasiparticle has been realized in condensed matter systems [50].…”