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arXiv:cond-mat/9607083 · Physical review. B, Condensed matter

Enhanced local moment formation in a chiral Luttinger liquid

Philip Phillips, Nancy Sandler

Published Jan 1, 1996• 13 citations
arXivHTMLPDF

Abstract

We derive here a stability condition for a local moment in the presence of an interacting sea of conduction electrons. The conduction electrons are modeled as a Luttinger liquid in which chirality and spin are coupled. We show that an Anderson $U$ defect in such an interacting system can be transformed onto a nearly Fermi-liquid problem. We find that correlations among the conduction electrons stabilize the local moment phase. A Schrieffer-Wolff transformation is then performed which results in an anisotropic exchange interaction indicative of the Kondo effect in a Luttinger liquid. The ground-state properties of this model are then equivalent to those of the Kondo model in a Luttinger liquid.

DOI
10.1103/physrevb.53.r468

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We derive here a stability condition for a local moment in the presence of an interacting sea of conduction electrons. The conduction electrons are modeled as a Luttinger liquid in which chirality and spin are coupled. We show that an Anderson UUU defect in such an interacting system can be transformed onto a nearly Fermi-liquid problem. We find that correlations among the conduction electrons stabilize the local moment phase. A Schrieffer-Wolff transformation is then performed which results in an anisotropic exchange interaction indicative of the Kondo effect in a Luttinger liquid. The ground-state properties of this model are then equivalent to those of the Kondo model in a Luttinger liquid.
The Kondo effect in a Luttinger liquid composed of right-moving, spin-up electrons and left-moving, spin-down electrons is mapped exactly onto the Kondo effect in a Fermi liquid. The transformation generates anisotropy in the exchange coupling, which explains the two most notable features of the Kondo effect in a full Luttinger liquid: the quenching of the impurity moment for ferromagnetic, as well as antiferromagnetic, exchange and a power-law dependence of the Kondo temperature on the exchange coupling. Impurity contributions to the low-energy thermodynamics have the same temperature dependence as in a Fermi liquid.
We present a one-dimensional model of electrons coupled to localized moments of spin S> 1S>~1S> 1 in which magnetism and superconductivity interplay in a nontrivial manner. This model has a non-Fermi-liquid ground state of the chiral spin liquid type. An unconventional odd-frequency pairing is shown to be the dominant instability of the system, together with antiferromagnetism of the local moments. We argue that this model captures the physics of the Kondo-Heisenberg spin S=1S=1S=1 chain, in the limit of strong Kondo coupling. Finally, we discuss briefly the effect of interchain coupling.
The effects of interchannel scattering of conduction electrons by the impurity and repulsion of conduction electrons at the impurity site on the two-channel Kondo model are simultaneously considered in this paper. It is shown that these two perturbations will substantially modify the usual local non-Fermi liquid behavior of the two-channel Kondo model. With bosonization and unitary transformations we find that the system can be transformed into a single channel Kondo model with anisotropy between longitudinal and transverse exchange couplings. Whatever for originally antiferromagnetic or ferromagnetic isotropic coupling, the system always flows to strong-coupling limit, which exhibits local Fermi liquid behavior at low temperatures.
A one-dimensional model of the modified Kondo lattice for $\ensuremath{\nu}$ degenerate conduction electrons interacting with the spin-12\frac{1}{2}21​ XXZ\mathrm{XXZ}XXZ Heisenberg chain is investigated. The model reduces to the $\mathrm{SU}(\ensuremath{\nu}+1)$-invariant anisotropic $t\ensuremath{-}J$ model with field splitting. The ground-state energy, the chemical potential, and the Fermi velocity of electrons have been calculated numerically for an arbitrary density of electrons. The model under consideration is characterized as a (marginal) Tomonago-Luttinger liquid described by c=1c=1c=1. We discuss the relevance of the results obtained to various theoretical treatments of the Kondo lattice model.
Interacting one-dimensional electron systems are generally referred to as ``Luttinger liquids,'' after the effective low-energy theory in which spin and charge behave as separate degrees of freedom with independent energy scales. The ``spin-incoherent Luttinger liquid'' describes a finite-temperature regime that is realized when the temperature is very small relative to the Fermi energy, but larger than the characteristic spin energy scale. Similar physics can take place in the ground state, when a Luttinger liquid is coupled to a spin bath, which effectively introduces a ``spin temperature'' through its entanglement with the spin degree of freedom. We show that the spin-incoherent state can be written as a factorized wave function, with a spin wave function that can be described within a valence bond formalism. This enables us to calculate exact expressions for the momentum distribution function and the entanglement entropy. This picture holds not only for two antiferromagnetically coupled $t\ensuremath{-}J$ chains, but also for the $t\ensuremath{-}J$-Kondo chain with strongly interacting conduction electrons. We argue that this theory is quite universal and may describe a family of problems that could be dubbed ``spin incoherent.''
To study the impurity potential effect to the Kondo problem in a Luttinger liquid, we introduce a model of ferromagnetic single-impurity Kondo problem in a multi-band one-dimensional δ-potential Fermi gas, which is exactly solvable for a special Kondo coupling constant via Bethe ansatz. It is found that the boundary potential modifies the local moment seriously due to the charge-spin coupling and the strong backward scattering off the impurity, and thus strongly affects the fixed point of the system. Generally, their is a residual entropy for the ground state which depends on the strength of the boundary potential. In addition, the tunneling effect through the impurity and the breakdown of the open boundary induced by the impurity are also discussed.