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The spatial dependence of spin and charge correlations in a one-dimensional, single impurity, Anderson model

James E. Gubernatis

Published Jan 1, 1986• 0 citations
OpenAlex

Abstract

Summarized are the results of a series of quantum Monte Carlo calculations of the spatial dependence of spin and charge correlations in a one-dimensional, single impurity, symmetric Anderson model. We corroborated several features of the model of Gubernatis, Hirsch, and Scalapino, and because we achieved lower temperatures, we were able to identify several additional unusual features in the behavior of the correlations as functions of U and ..beta... We also showed the existence of a charge compensation sum role and found a power law decay of the correlations at low temperatures.

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Summarized are the results of a series of quantum Monte Carlo calculations of the spatial dependence of spin and charge correlations in a one-dimensional, single impurity, symmetric Anderson model. We corroborated several features of the model of Gubernatis, Hirsch, and Scalapino, and because we achieved lower temperatures, we were able to identify several additional unusual features in the behavior of the correlations as functions of U and ..beta... We also showed the existence of a charge compensation sum role and found a power law decay of the correlations at low temperatures.
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Quantum Monte Carlo[MC] calculation of one-dimensional periodic Anderson model without orbital degeneracy is performed by use of the path-integral formulation. Local f moment coincides well with the recent MC calculation for single impurity by Hirsch and Fye above the temperature at which antiferromagnetic correlation starts to grow, and decreases faster than those for single impurity and coupled two impurities below that temperature. Overall features, including susceptibilities, resemble one-dimensional Hubbard model with half-filled band.
We study by Monte Carlo simulations a magnetic impurity coupled antiferromagnetically to a one-dimensional quantum spin model. The impurity susceptibility and the spin-correlation function are calculated. By defining and evaluating an energy scale from the inverse of the impurity susceptibility at zero temperature, we find a scaling relation for the impurity susceptibility in agreement with the prediction of the conformal field theory. We analyze the problem by mapping the spin model onto the resonant-level model, and interpret the energy scale as the resonant-level width. The spin-correlation function between the impurity spin and the spins in the chain is found to extend over long range at low temperatures. We show that the system can be considered as a model of an insulator with heavy-fermion behavior.
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A magnetic moment in a metal or in a quantum dot is, at low temperatures, screened by the conduction electrons through the mechanism of the Kondo effect. This gives rise to spin-spin correlations between the magnetic moment and the conduction electrons, which can have a substantial spatial extension. We study this phenomenon, the so-called Kondo cloud, by means of the density matrix renormalization group method for the case of the single-impurity Anderson model. We focus on the question whether the Kondo screening length, typically assumed to be proportional to the inverse Kondo temperature, can be extracted from the spin-spin correlations. For several mechanisms -- the gate potential and a magnetic field -- that destroy the Kondo effect, we investigate the behavior of the screening cloud induced by these perturbations.
Using variational matrix product states, we analyze the finite temperature behavior of a half-filled periodic Anderson model in one dimension, a prototypical model of a Kondo insulator. We present an extensive analysis of single-particle Green’s functions, two-particle Green’s functions, and transport functions creating a broad picture of the low-temperature properties. We confirm the existence of energetically low-lying spin excitations in this model and study their energy-momentum dispersion and temperature dependence. We demonstrate that charge-charge correlations at the Fermi energy exhibit a different temperature dependence than spin-spin correlations. While energetically low-lying spin excitations emerge approximately at the Kondo temperature, which exponentially depends on the interaction strength, charge correlations vanish already at high temperatures. Furthermore, we analyze the charge and thermal conductivity at finite temperatures by calculating the time-dependent current-current correlation functions. While both charge and thermal conductivity can be fitted for all interaction strengths by gapped systems with a renormalized band gap, the gap in the system describing the thermal conductivity is generally smaller than the system describing the charge conductivity. Thus, two-particle correlations affect the charge and heat conductivities in a different way resulting in a temperature region where the charge conductivity of this one-dimensional Kondo insulator is already decreasing while the heat conductivity is still increasing.