Symmetric single-impurity Kondo model on a tight-binding chain: a comparison of analytical and numerical ground-state approaches
| Autor: | Barcza, Gergely, Bauerbach, Kevin, Eickhoff, Fabian, Anders, Frithjof B., Gebhard, Florian, Legeza, Örs |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Phys. Rev. B 101, 075132 (2020) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevB.101.075132 |
| Popis: | We analyze the ground-state energy, local spin correlation, impurity spin polarization, impurity-induced magnetization, and corresponding zero-field susceptibilities of the symmetric single-impurity Kondo model on a tight-binding chain with bandwidth $W=2{\cal D}$ and coupling strength $J_{\rm K}$. We compare perturbative results and variational upper bounds from Yosida, Gutzwiller, and first-order Lanczos wave functions to the numerically exact data obtained from the Density-Matrix Renormalization Group (DMRG) and from the Numerical Renormalization Group (NRG) methods. The Gutzwiller variational approach becomes exact in the strong-coupling limit and reproduces the ground-state properties from DMRG and NRG for large couplings. We calculate the impurity spin polarization and its susceptibility in the presence of magnetic fields that are applied globally/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 $J_{\rm K}/{\cal D}\approx 0.5$. For smaller Kondo couplings, only the NRG provides reliable results for a general host-electron density of states $\rho_0(\epsilon)$. To compare with results from Bethe Ansatz, we study the impurity-induced magnetization and zero-field susceptibility. For small Kondo couplings, the zero-field susceptibilities at zero temperature approach $\chi_0(J_{\rm K}\ll {\cal D})/(g\mu_{\rm B})^2\approx \exp[1/(\rho_0(0)J_{\rm K})]/(2C{\cal D}\sqrt{\pi e \rho_0(0)J_{\rm K}})$, 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 $\rho_0(0)J_{\rm K}$. Comment: 66 pages (26 pages main text, 12 pages appendices, 28 pages supplemental material), 23 figures |
| Databáze: | arXiv |
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