We study the effect of disorder in strongly interacting small atomic chains. Using the Kotliar-Ruckenstein slave-boson approach, we diagonalize the Hamiltonian via scattering matrix theory. We numerically solve the Kondo transmission and the slave-boson parameters that allow us to calculate the Kondo temperature. We demonstrate that in the weak disorder regime, disorder in the energy levels of the dopants induces a nonscreened disorder in the Kondo couplings of the atoms. We show that disorder increases the Kondo temperature of a perfect chain. We find that this disorder in the couplings comes from a local distribution of Kondo temperatures along the chain. We propose two experimental setups where the impact of local Kondo temperatures can be observed.
We study the effect of disorder in strongly interacting small atomic chains. Using the Kotliar-Ruckenstein slave-boson approach, we diagonalize the Hamiltonian via scattering matrix theory. We numerically solve the Kondo transmission and the slave-boson parameters that allow us to calculate the Kondo temperature. We demonstrate that in the weak disorder regime, disorder in the energy levels of the dopants induces a nonscreened disorder in the Kondo couplings of the atoms. We show that disorder increases the Kondo temperature of a perfect chain. We find that this disorder in the couplings comes from a local distribution of Kondo temperatures along the chain. We propose two experimental setups where the impact of local Kondo temperatures can be observed.
We introduce a minimal effective framework designed to address the anomalous low-temperature thermodynamics observed in strongly disordered interacting systems near a metal-insulator transition, such as doped semiconductors. Our approach examines how a strongly inhomogeneous electronic bath quenches dilute pairs of local magnetic moments. By solving the resulting two-impurity Kondo-Heisenberg problem within a large-N variational framework, we capture the competition between Kondo screening and random-singlet formation. Both mechanisms give rise to singular thermodynamic responses, producing a magnetic susceptibility of the form χ(T)∼T−α, where the exponent α evolves smoothly with model parameters and saturates in the metallic regime, consistent with experimental observations. Our results establish a unified framework that connects random-singlet physics and disorder-induced Kondo screening in strongly disordered correlated materials.
We study an exotic Kondo effect in a system consisting of two one-dimensional XX Heisenberg ferromagnetic spin-1/2 chains (denoted by α=u,d for up and down chains) coupled to a quantum dot consisting of two localized spin-1/2 magnets. Using the Jordan–Wigner transformation on the Heisenberg Hamiltonian of the two chains, this system can be expressed in terms of non-interacting spinless fermionic quasiparticles. As a result, the Hamiltonian of the whole system is expressed as an Anderson model for spin-1/2 fermions interacting with a spin-1/2 impurity. Thus, we study the scattering of fermionic quasiparticles (propagating along spin chains) by a pair of localized magnetic impurities. At low temperature, the localized spin-1/2 magnets are shielded by the chain “spins” via the Kondo effect. We calculate the Kondo temperature TK and derive the temperature dependence of the entropy, the specific heat and the “magnetic susceptibility” of the dot for T≫TK. Our results can be generalized to the case of antiferromagnetic XX chains.
It is well known that the free electron Kondo problem can be described by a one-dimensional (1D) model because only the s-wave part of the electronic wavefunction is affected by the Kondo coupling. Moreover, since only the spin degrees of freedom are involved in the Kondo interaction, and due to spin–charge separation in 1D, the universal low energy long distance physics of the Kondo model also arises when a magnetic impurity is coupled to the end of a gapless antiferromagnetic J 1 –J 2 spin- chain, where J 1 ( J 2 ) is the (next) nearest neighbor coupling. Experimental realizations of such spin chain models are possible and, using various analytical and numerical techniques, we present a detailed and quantitative comparison between the usual free electron Kondo model and such spin chain versions of the Kondo problem. For the gapless J 1 –J 2 spin chain two cases are studied, with zero next nearest neighbor coupling, J 2 = 0, and with a critical second-neighbor coupling, J 2 = J 2 c . We first focus on the spin chain impurity model with a critical second-neighbor antiferromagnetic exchange where a bulk marginal coupling present in the spin chain model for J 2 < J 2 c vanishes . There, the usual Kondo physics is recovered in the spin chain model in the low energy regime (up to negligible corrections, dropping as powers of inverse length or energy). At J 2 c the spin chain model is not exactly solvable and we demonstrate the equivalence to the Kondo problem by comparing density matrix renormalization group calculations on the frustrated spin chain model with exact Bethe ansatz calculations of the electronic Kondo problem. We then analyze the nearest neighbor model ( J 2 = 0) where a new kind of Kondo effect occurs due to the presence of the bulk marginal coupling. This marginal coupling slightly alters the β function for the Kondo coupling, leading to a slower variation of the Kondo temperature, T K , with the bare Kondo coupling. In their exact Bethe ansatz solution of this spin chain impurity model ( J 2 = 0), Frahm and Zvyagin noted this relation as well as the connection to the Kondo problem. Here, by numerically solving the Bethe ansatz equations we provide further evidence for the connection to Kondo physics and in addition we present low temperature quantum Monte Carlo results for the impurity susceptibility that further support this connection.
Abstract We investigate the boundary phenomena that arise in a finite-size XX spin chain interacting through an XX interaction with a spin − 1 2 impurity located at its edge. Upon Jordan–Wigner transformation, the model is described by a quadratic Fermionic Hamiltonian. Our work displays, within this ostensibly simple model, the emergence of the Kondo effect, a quintessential hallmark of strongly correlated physics. We also show how the Kondo cloud shrinks and turns into a single particle bound state as the impurity coupling increases beyond a critical value. In more detail, using both Bethe Ansatz and exact diagonalization techniques, we show that the local moment of the impurity is screened by different mechanisms depending on the ratio of the boundary and bulk coupling J imp J . When the ratio falls below the critical value 2 , the impurity is screened via the Kondo effect. However, when the ratio between the coupling exceeds the critical value 2 an exponentially localized bound mode is formed at the impurity site which screens the spin of the impurity in the ground state. We show that the boundary phase transition is reflected in local ground state properties by calculating the spinon density of states, the magnetization at the impurity site in the presence of a global magnetic field, and the finite temperature susceptibility of the impurity. We find that the spinon density of states in the Kondo phase has the characteristic Lorentzian peak that moves from the Fermi level to the maximum energy of the spinon as the impurity coupling is increased and becomes a localized bound mode in the bound mode phase. Moreover, the impurity magnetization and the finite temperature impurity susceptibility behave differently in the two phases. When the boundary coupling J imp exceeds the critical value 2 J , the model is no longer boundary conformal invariant as a massive bound mode appears at the impurity site.
We analyze the crossover from Kondo to weak-link regime by means of a model of tunable bond impurities in the middle of a spin-1/2 XXZ Heisenberg chain. We study the Kondo screening cloud and estimate the Kondo length by combining perturbative renormalization group approach with the exact numerical calculation of the integrated real-space spin-spin correlation functions. We show that, when the spin impurity is symmetrically coupled to the two parts of the chain with realistic values of the Kondo coupling strengths and spin-parity symmetry is preserved, the Kondo length takes values within the reach of nowadays experimental technology in ultracold-atom setups. In the case of nonsymmetric Kondo couplings and/or spin parity broken by a nonzero magnetic field applied to the impurity, we discuss how Kondo screening redistributes among the chain as a function of the asymmetry in the couplings and map out the shrinking of the Kondo length when the magnetic field induces a crossover from Kondo impurity to weak-link physics.
Exactly solvable Kondo problem in the open t−J chains
We study the problem of a boundary magnetic impurity coupled with the solvable t−J chains. Our model provides a good start point to understand the Kondo problem in a Luttinger liquid as well as in a strongly correlated host. The Kondo coupling constant J can take arbitrary values, which allows us to study the ferromagnetic and antiferromagnetic Kondo problems simultaneously. It is shown that both the Kondo coupling and the scalar potential effectively reconcile the spin dynamics at low temperatures. Generally, the impurity spin is split into two ghost spins via coupling effect. The residual entropy, which can be exactly derived for the present model, is strongly interaction-dependent. This hints the local spin configuration is very complicated and very different from that in the conventional Kondo problem. An unscreening phenomenon in the antiferromagnetic regime is found, which reveals the impurity potential plays an important role for the Kondo problem in a strongly correlated host. The low temperature specific heat is calculated in the framework of local Landau-Luttinger liquid theory.