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arXiv:cond-mat/0509407 · Physical Review B

Fermi edge singularity in the SU (N) Wolff model

Balázs Dóra

Published Mar 23, 2006• 2 citations
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Abstract

The low-temperature properties of the SU$(N)$ Wolff impurity model are studied via Abelian bosonization. The path integral treatment of the problem allows for an exact evaluation of low-temperature properties of the model. The single-particle Green's function is enhanced due to the presence of local correlation. The basic correlation functions such as the charge or spin correlator are also influenced by the presence of impurity, and show local Fermi liquid behavior. The x-ray absorption is affected by the presence of the local Hubbard interaction. The exponent is decreased (increased) for repulsive (attractive) interactions.

DOI
10.1103/physrevb.73.125113

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The low-temperature properties of the SU(N)(N)(N) Wolff impurity model are studied via Abelian bosonization. The path integral treatment of the problem allows for an exact evaluation of low-temperature properties of the model. The single-particle Green's function is enhanced due to the presence of local correlation. The basic correlation functions such as the charge or spin correlator are also influenced by the presence of impurity, and show local Fermi liquid behavior. The x-ray absorption is affected by the presence of the local Hubbard interaction. The exponent is decreased (increased) for repulsive (attractive) interactions.
Abelian bosonization is applied to a magnetic impurity model, the so-called Wolff impurity model. The resulting bosonized version of the model can be solved exactly. We calculate the local dynamic spin and charge density-density correlations of the conduction electrons, and show that a quasi-particle peak in the spin-density excitations appears and becomes sharp significantly as the local interaction U grows up. The local static spin and charge susceptibilities and specific heat of the interacting electrons are also obtained, explicitly displaying a local Fermi liquid behavior.
While much is known about repulsive quantum impurity models, significantly less attention has been devoted to their attractive counterparts. This motivated us to study the attractive SU(N) Anderson impurity model. While for the repulsive case the phase diagram features mild N dependence and the ground state is always a Fermi liquid, in the attractive case a Kosterlitz-Thouless charge localization phase transition is revealed for N>2. Beyond a critical value of attractive interaction, an abrupt jump appears in the number of particles at the impurity site, and a singular Fermi liquid state emerges, where the scattering of quasiparticles is found to exhibit power law behavior with fractional power. The capacity diverges exponentially at the quantum critical point, signaling the Kosterlitz-Thouless transition.
We report the exact calculation of the Fermi-edge singularity exponent for correlated electrons in one dimension (Luttinger liquid). Focusing on the special interaction parameter g=1/2g=1/2g=1/2, the asymptotic long-time behavior can be obtained using the Wiener-Hopf method. The result confirms the previous assumption of an open boundary fixed point. In addition, a dynamic kkk-channel Kondo impurity is studied via Abelian bosonization for k=2k=2k=2 and k=4k=4k=4. It is shown that the corresponding orthogonality exponents are related to the orthogonality exponent in a Luttinger liquid.
We consider the one-dimensional gas of fermions with spin S interacting via an attractive δ -function potential using the Bethe Ansatz solution. In zero magnetic field the atoms form bound states of N = 2 S + 1 fermions, i.e. generalized Cooper states with each atom having a different spin component. For low energy excitations the system is a Luttinger liquid and is properly described by a conformal field theory with conformal charge c = 1 . The linear dispersion of a Luttinger liquid is asymptotically exact in the low-energy limit where the band curvature terms in the dispersion are irrelevant. For higher energy excitations, however, the spectral function displays deviations in the neighborhood of the single-particle (hole) energy, which can be described by an effective X-ray edge type model. Using the Bethe Ansatz solution we obtain expressions for the critical exponents for the single-particle (hole) Green's function. This model can be relevant in the context of ultracold atoms with effective total spin S confined to an elongated optical trap.
We study the electrical and thermal transport through the SU(N)(N)(N) Wolff model with the use of bosonization. The Wilson ratio reaches unity as NNN grows to infinity. The electric conductance is dominated by the charge channel, and decreases monotonically with increasing interaction. The thermal conductivity enhances in the presence of a local Hubbard UUU. The Wiedemann-Franz law is violated; the Lorentz number depends strongly on the interaction parameter, which can be regarded as a manifestation of spin-charge separation.