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International Journal of Modern Physics B

STATIC AND DYNAMICAL PROPERTIES OF A SINGLE IMPURITY IN A STRONGLY CORRELATED HOST

Ajay Nandgaonkar, P. Durganandini, Mihir Arjunwadkar, D. G. Kanhere

Published Mar 20, 1999• 0 citations
Publisher

Abstract

We study, using numerical exact diagonalisation, some static and dynamical properties of a single impurity substituted into a one-dimensional repulsive Hubbard chain. A systematic scan of the parameter-space reveals a rich magnetic phase diagram. Interactions on the lattice stabilize the local moment phase of the impurity. A scalar impurity is seen to induce local moments on the neighbouring sites near Half Filling. Static spin and charge correlation functions reflect a non-Fermi liquid character of the ground state in the presence of a scalar impurity.

DOI
10.1142/s0217979299000679

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We study, using numerical exact diagonalisation, some static and dynamical properties of a single impurity substituted into a one-dimensional repulsive Hubbard chain. A systematic scan of the parameter-space reveals a rich magnetic phase diagram. Interactions on the lattice stabilize the local moment phase of the impurity. A scalar impurity is seen to induce local moments on the neighbouring sites near Half Filling. Static spin and charge correlation functions reflect a non-Fermi liquid character of the ground state in the presence of a scalar impurity.
Using numerical techniques we study the zero-temperature properties of a substitutional magnetic impurity in a one-dimensional correlated system described by the Hubbard model with repulsive interaction U. We find that, while the static spin correlation maintains a 2kF{\mathit{k}}_{\mathit{F}}kF​ periodicity, the charge correlations show Friedel oscillations with a 4kF{\mathit{k}}_{\mathit{F}}kF​ periodicity for large values of U. The static on-site susceptibility decreases as the interactions in the chain are turned on and we interpret this as an increase of the Kondo temperature. For large values of U the short-range antiferromagnetic correlations dominate over the collective Kondo singlet formation.
The exact phase diagrams of the one-dimensional Hubbard model, both attractive and repulsive, in the presence of an arbitrary magnetic field h for various electron concentrations n and on-site interaction strengths U <0 or U >0 are calculated and investigated. The exact ground-state properties, namely, the ground-state energy, the average spin (magnetization), the concentration of the doubly occupied sites, the kinetic energy, the chemical potential, the spin (magnetic) susceptibility and the charge compressibility, are calculated and examined over a wide range of interaction strengths U for various h and n . It is found that the spin susceptibility at half-filling is non-analytic and changes discontinuously as U →0. The exact theory shows the absence of a charge energy gap in the U ⩽0 region for all n and provides, for the chemical potential, the rigorous upper and lower bounds for half-filled and empty bands respectively. The analytical results derived for the weak-coupling limit and asymptotic expansions for strong coupling are in full agreement with the numerical calculations.
We investigate the single-band Hubbard model with random site energies in the strong-repulsion limit, as represented by the slave-boson formulation of the t-J model. It is essential to include the correlations between the slave-boson mean field and the disorder. This leads to the widening of the non-Fermi-liquid (``generalized Mott insulating'') region around half filling. In the Fermi-liquid regime we apply the renormalization-group method. The resulting phase diagram has superconducting, magnetic, and insulating phases. The disorder generally suppresses superconductivity and gives rise to the formation of localized magnetic moments.
The Hubbard chain with a magnetic impurity of arbitrary spin SSS is studied using the Bethe ansatz technique. We consider two kinds of impurities which interact with itinerant electrons on the neighboring lattice sites without destroying the integrability. The correlations in the host always induce valence fluctuations at the impurity site. For a repulsive Hubbard UUU, an impurity coupled via antiferromagnetic exchange to the host reveals magnetic properties similar to those of the ordinary Kondo effect. In contrast, a hybridization impurity (Anderson-like) embedded into the attractive Hubbard model gives rise to essentially different magnetic behavior. This difference is a consequence of the spin gap in the host.
Attractive non-local interactions jointly with repulsive local interaction in a microscopic modelling of electronic Fermi liquids generate a competition between an enhancement of the static charge susceptibility–ultimately signalling charge instability and phase separation–and its correlation induced suppression. We analyse this scenario through the investigation of the extended Hubbard model on a two-dimensional square lattice, using the spin rotation invariant slave-boson representation of Kotliar and Ruckenstein. The quasiparticle density of states, the renormalised effective mass and the Landau parameter F s 0 are presented, whereby the positivity of F s 0 – 1 constitutes a criterion for stability. Van Hove singularities in the density of states support possible charge instabilities. A (negative) next-nearest neighbour hopping parameter t' shifts their positions and produces a tendency towards charge instability even for low filling whereas the t' -controlled particle-hole asymmetry of the correlation driven effective mass is small. A region of instability on account of the attractive interaction V is identified, either at half filling in the absence of strong electronic correlations or, in the case of large on-site interaction U , at densities far from half filling.
We explore the two-dimensional extended Hubbard model on the triangular lattice in the high doping regime. On-site and nearest-neighbour repulsive interactions are treated in a non-perturbative way by means of Extended Dynamical Mean Field Theory. We compute the low-temperature phase diagram, displaying a metallic phase and a symmetry-broken phase for strong intersite repulsions. We describe the correlation effects on both single-particle and two-particle observables in the metallic phase. Whereas single-particle spectra feature a Hubbard satellite typical of strongly correlated systems, local susceptibilities remain close to their non-interacting limit, even for large on-site repulsions. We argue that this behaviour is typical of the strongly doped case. We also report a region in parameter space with negative static local screening.