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Kuwait Journal of Science

Ground state magnetic susceptibility of Kondo impurities

Bedoor Alkurtass

Published Jun 5, 2024• 1 citation
Publisher

Abstract

Impurity models describe localized impurities interacting with the spins of electrons. Strong correlations lead to non-trivial behaviours of the model. In this work we present 3 different impurity models: (1) the single-impurity Kondo model; (2) the two-impurity Kondo model; (3) the two-channel Kondo model. For each model we present a spin chain emulation and utilize the density matrix renormalization group (DMRG). We study the magnetization and zero-temperature susceptibility of the impurity when a local magnetic field is applied. We get the expected relations theoretically.

DOI
10.1016/j.kjs.2024.100269

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Impurity models describe localized impurities interacting with the spins of electrons. Strong correlations lead to non-trivial behaviours of the model. In this work we present 3 different impurity models: (1) the single-impurity Kondo model; (2) the two-impurity Kondo model; (3) the two-channel Kondo model. For each model we present a spin chain emulation and utilize the density matrix renormalization group (DMRG). We study the magnetization and zero-temperature susceptibility of the impurity when a local magnetic field is applied. We get the expected relations theoretically.
The Kondo model describes a magnetic impurity in a metallic host. Here, the authors use variational approaches (Lanczos, Yosida, Gutzwiller) and quasi-exact numerical techniques (numerical renormalization group, density matrix renormalization group) to study the ground-state energy and magnetization, and compare these properties to Bethe ansatz results. The Gutzwiller wave function is an excellent trial state for strong coupling. For weak coupling, the numerical renormalization group gives the best description of the magnetic properties. A combination of Bethe ansatz and perturbation theory provides new benchmark results for the zero-field susceptibility.
By making use of the Lanczos and the density-matrix renormalization-group methods, we study the zero-temperature properties of a spin-1/2 antiferromagnetic Heisenberg chain system with a spin-1/2 magnetic impurity symmetrically coupled to its two nearest-neighbor spins. A comparison is made with the results for a magnetic impurity coupled only to the nearest-neighbor spin in the chain. The binding energy and the spin correlations are calculated. The matrix elements of the impurity spin operators are also calculated between several low-energy states. By carefully analyzing finite-size effects, we show that the dynamical structure factor of the impurity contains a \ensuremath{\delta}-function contribution at zero frequency which does not vanish in the thermodynamic limit for the case of symmetrical coupling. This indicates a partial decoupling of the impurity spin from the spins in the chain, and therefore the impurity susceptibility is predicted to show a Curie behavior. This contradicts the two-channel Kondo behavior suggested from analytic considerations.
We consider a magnetic impurity in the antiferromagnetic spin- 1/21/21/2 chain which is equivalent to the two-channel Kondo problem in terms of the field theoretical description. Using a modification of the transfer-matrix density matrix renormalization group we are able to determine the crossover function for the impurity susceptibility over a large temperature range, which exhibits universal data collapse. We also calculate the local susceptibilities near the impurity, which show an interesting competition of boundary effects. This results in quantitative predictions for experiments on doped spin- 1/21/21/2 chains, which could observe two-channel Kondo physics directly.
We study the ground state properties of a single magnetic impurity in the honeycomb lattice. To understand the non-perturbative properties, we use the density matrix renormalization group method where the honeycomb lattice model is mapped onto an effective one-dimensional model by means of the Lanczos recursion technique. We apply this method to three different models: (i) a magnetic adatom on the honeycomb lattice, (ii) a substitutional magnetic impurity in the honeycomb lattice, and (iii) a defect in the honeycomb lattice. Here, we focus only on the particle-hole symmetric cases and find that the ground state of model (i) is qualitatively different from the others: the magnetic impurity spin behaves like an isolated spin in model (i) while it is screened in models (ii) and (iii) by conduction electrons to form a Kondo singlet like state.