Symmetric single-impurity Kondo model on a tight-binding chain: Comparison of analytical and numerical ground-state approaches

Abstract

We analyze the ground-state energy, local spin correlation, impurity spin polarization, impurityinduced magnetization, and corresponding zero-field susceptibilities of the symmetric single-impurity Kondo model (SIKM) on a tight-binding chain with bandwidth W = 2D where a spin-1/2 impurity at the chain center interacts with coupling strength JK with the local spin of the bath electrons. We compare perturbative results and variational upper bounds from Yosida, Gutzwiller, and first-order Lanczos wave functions to the numerically exact extrapolations obtained from the Density-Matrix Renormalization Group (DMRG) method and from the Numerical Renormalization Group (NRG) method performed with respect the inverse system size and Wilson parameter, respectively. In contrast to the Lanczos and Yosida wave functions, the Gutzwiller variational approach becomes exact in the strong-coupling limit, JK ≫ W , and reproduces the ground-state properties from DMRG and NRG for large couplings, JK W , with a high accuracy. For weak coupling, the Gutzwiller wave function describes a symmetry-broken state with an oriented local moment, in contrast to the exact solution. We calculate the impurity spin polarization and its susceptibility in the presence of magnetic fields that are applied globally or only locally to the impurity spin. The Yosida wave function provides qualitatively correct results in the weak-coupling limit. In DMRG, chains with about 10 3 sites are large enough to describe the susceptibilities down to JK/D ≈ 0.5. For smaller Kondo couplings, only the NRG provides reliable results for a general host-electron density of states ρ0(ǫ). To compare with results from Bethe Ansatz that become exact in the wideband limit, we study the impurity-induced magnetization and zero-field susceptibility. For small Kondo couplings, the zero-field susceptibilities at zero temperature approach χ0(JK ≪ D)/(gµB) 2 ≈ exp[1/(ρ0(0)JK)]/(2CD πeρ0(0)JK), where ln(C) is the regularized first inverse moment of the density of states. Using NRG, we determine the universal sub-leading corrections up to second order in ρ0(0)JK.

Thermodynamics and Screening in the Ising–Kondo Model

“…For a thorough discussion of the difference between the impurity‐induced magnetization, , and the impurity spin polarization, , see previous studies. [ 17,18 ]…”

“…Using Mathematica [ 22 ] we find and so that for up to and including second order in . Using perturbation theory in , [ 7,18 ] it is readily shown that is indeed independent of the host electron density of states up to second order in . Equation (80) and (81) show that small magnetic fields induce small corrections, of the order .…”

Real-space numerical renormalization-group computation of transport properties in the side-coupled geometry

“…While the diagonalization of the odd term (11) of the model Hamiltonian is straightforward, the even term (10) requires numerical treatment. Brute-force diagonalization is possible for small lattices.…”

“…Substitution of H f λ for H f yields a discretized approximation to the Hamiltonian H A . Equation (10) becomes…”

“…These developments and subsequent advances have converted the method into an apt instrument in the rapidly growing area of nano-device development [5]. Numerous examples constitute recent literature [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24].…”