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Acta Physica Sinica

STUDY ON THE SINGLE IMPURITY SCATTERING TO THE ONE DIMENSIONAL SPIN 1/2 ELECTRONS

Un L

Published Jan 1, 1997• 0 citations
OpenAlex

Abstract

Abstract The Gaussian wave functional method is applied to investigate the effects of the scattering of a local impurity to the one dimensional conduction electrons,whose low energy behavior can be described by the Luttinger model. Our results show that both the single particle scattering and pair particle scattering are important in this case. The competition between these two scattering mechanisms gives rise to the renormalized masses for both charge and spin density waves. The vanishing of these masses depicts the phase boundaries in the parameter space,different dynamical behaviors are thus determined.

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STUDY ON THE SINGLE IMPURITY SCATTERING TO THE ONE DIMENSIONAL SPIN 1/2 ELECTRONS

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The Gaussian wave functional method is applied to investigate the effects of the scattering of a local impurity to the one dimensional conduction electrons,whose low energy behavior can be described by the Luttinger model. Our results show that both the single particle scattering and pair particle scattering are important in this case. The competition between these two scattering mechanisms gives rise to the renormalized masses for both charge and spin density waves. The vanishing of these masses depicts the phase boundaries in the parameter space,different dynamical behaviors are thus determined.

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In one-dimensional quantum wires the interplay of electron correlations and impurities strongly influences the low-energy physics. The diversity of energy scales and the competition of correlations in interacting Fermi systems can be treated very efficiently with the functional renormalization group (fRG), describing the gradual evolution from a microscopic model Hamiltonian to the effective low-energy action as a function of a continuously decreasing energy cutoff. The fRG provides the universal low-energy asymptotics as well as nonuniversal properties, and in particular an answer to the important question at what scale the ultimate asymptotics sets in. We investigate the influence of impurities on spectral and transport properties of fermionic lattice models with short-range interactions. The results capture relevant energy scales and crossover phenomena, in addition to the universal low-energy asymptotics. For weak and intermediate impurity strengths the asymptotic behavior is approached only at rather low energy scales, accessible only for very large systems. For spin-1/2 systems two-particle backscattering leads to striking effects, which are not captured if the bulk system is approximated by its low-energy fixed point, the Luttinger model. In particular, the expected decrease of spectral weight near the impurity and of the conductance at low energy scales is often preceded by a pronounced increase, and the asymptotic power laws are modified by logarithmic corrections.

arXiv:cond-mat/0603341•Jan 1, 2006•4 citations
Abstract The Gaussian wave functional method is applied to investigate the effects of the scattering of a local impurity to the one dimensional conduction electrons,whose low energy behavior can be described by the Luttinger model. Our results show that both the single particle scattering and pair particle scattering are important in this case. The competition between these two scattering mechanisms gives rise to the renormalized masses for both charge and spin density waves. The vanishing of these masses depicts the phase boundaries in the parameter space,different dynamical behaviors are thus determined.
The Gaussian wave functional method is applied to investigate the effects of the scattering of a local impurity to the one dimensional conduction electrons,whose low energy behavior can be described by the Luttinger model. Our results show that both the single particle scattering and pair particle scattering are important in this case. The competition between these two scattering mechanisms gives rise to the renormalized masses for both charge and spin density waves. The vanishing of these masses depicts the phase boundaries in the parameter space,different dynamical behaviors are thus determined.
We review some of our recent results on the potential scattering in a weakly interacting one-dimensional(1D) electron gas. The technique we developed is a poor man's renormalization group procedure in the scattered wave basis. This technique can treat the renormalizations of the scattering on the barrier and the scattering between the electrons in a coherent way, and it allows us to find the scattering amplitudes on a localized potential of arbitrary strength for electrons at any energy. The obtained phase shifts are used to study the Fermi-edge singularity in an interacting 1D electron system, where anomalous exponent of the power-law singularity in the vicinity of the edge is found. The transmission coefficient is directly related to the conductance of a 1D channel by the Landauer formula. Simple formulas that describe the conductance at any temperature are derived. In spin-[Formula: see text] systems, the electron–electron backscattering induces renormalizations of the interaction constants, which causes the low-temperature conductance to deviate from the results of the Luttinger liquid theory. In particular, the temperature dependence of the conductance may become nonmonotonic. In the presence of a magnetic field, backscattering gives rise to a peak in the differential conductance at bias equal to the Zeeman splitting.
We analyze the one-dimensional extended Hubbard model with a single static impurity by using a computational technique based on the functional renormalization group. This extends previous work for spinless fermions to spin-1∕21∕21∕2 fermions. The underlying approximations are devised for weak interactions and arbitrary impurity strengths, and have been checked by comparing with density-matrix renormalization-group data. We present results for the density of states, the density profile, and the linear conductance. Two-particle backscattering leads to striking effects, which are not captured if the bulk system is approximated by its low-energy fixed point, the Luttinger model. In particular, the expected decrease of spectral weight near the impurity and of the conductance at low energy scales is often preceded by a pronounced increase, and the asymptotic power laws are modified by logarithmic corrections.
We study the low-temperature properties of a spin-1/2 magnetic impurity coupled to a one-dimensional interacting electron system. Using a formalism by Affleck and Ludwig, with a scale invariant boundary condition replacing the impurity, we exploit boundary conformal field theory to deduce the impurity thermal and magnetic response. In the case of only forward electron scattering off the impurity, we predict the same critical scaling as for the two-channel Kondo effect for noninteracting electrons, but with a different Wilson ratio. Backward electron scattering off the impurity destabilizes this behavior and drives the system to a new fixed point. In the case of equal amplitudes for forward and backward scattering (Kondo interaction), we show that there are only two types of scaling behaviors consistent with the symmetries of the problem: either a local Fermi liquid or a critical theory with an anomalous specific heat. The latter case agrees with a recent poor-man's scaling result proposed by Furusaki and Nagaosa. \textcopyright{} 1996 The American Physical Society.
In one-dimensional quantum wires the interplay of electron correlations and impurities strongly influences the low-energy physics. The diversity of energy scales and the competition of correlations in interacting Fermi systems can be treated very efficiently with the functional renormalization group (fRG), describing the gradual evolution from a microscopic model Hamiltonian to the effective low-energy action as a function of a continuously decreasing energy cutoff. The fRG provides the universal low-energy asymptotics as well as nonuniversal properties, and in particular an answer to the important question at what scale the ultimate asymptotics sets in. We investigate the influence of impurities on spectral and transport properties of fermionic lattice models with short-range interactions. The results capture relevant energy scales and crossover phenomena, in addition to the universal low-energy asymptotics. For weak and intermediate impurity strengths the asymptotic behavior is approached only at rather low energy scales, accessible only for very large systems. For spin-1/2 systems two-particle backscattering leads to striking effects, which are not captured if the bulk system is approximated by its low-energy fixed point, the Luttinger model. In particular, the expected decrease of spectral weight near the impurity and of the conductance at low energy scales is often preceded by a pronounced increase, and the asymptotic power laws are modified by logarithmic corrections.