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Theoretical and Mathematical Physics

Hamiltonian structures for integrable field theory models. II. Models with O(n) and Sp(2k) symmetry on a one-dimensional lattice

Nicolai Reshetikhin

Published May 1, 1985• 10 citations
Publisher
DOI
10.1007/bf01017901

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The multichannel Kondo model exhibits non-Fermi-liquid behavior in the overscreened case, when the number of channels, k, is greater than twice the size of the impurity spin, s. We show that, for overscreening, exchange anisotropy is irrelevant at the low-temperature fixed point for s=1/2 or s=k/2-1/2, but relevant for all other values of s. However, an external field or channel asymmetry is relevant, producing crossover to Fermi-liquid fixed points with different phase shifts for each spin in the first case and for each channel in the second. These results are elucidated by explicit comparison of analytic finite-size spectra derived from conformal field theory with those obtained from numerical renormalization-group calculations. The relevance of the results (for k=2 and s=1/2) to the quadrupolar Kondo Hamiltonian (which has been proposed as a model for many uranium-based heavy-fermion materials) will be briefly discussed. Also, a larger, a/Isymplectic symmetry Sp(2k) is shown to be present in the k-channel Kondo model.

Physical review. B, Condensed matter•Apr 1, 1992•204 citations
A disordered fermion model defined on a two-dimensional square lattice with $\ensuremath{\pi}$ flux is studied. Time-reversal symmetry and one of four possible chiral symmetries are imposed. The continuum limit of the model near zero energy yields Dirac fermions with chiral symmetry. It is shown that one of them has $\mathrm{Sp}(n)\ifmmode\times\else\texttimes\fi{}\mathrm{Sp}(n)$ symmetry whereas others have U(2n)(2n)(2n) symmetry, both of which are broken to Sp(n),(n),(n), and the fluctuation around a saddle point is described, respectively, by the Sp(n)2{(n)}_{2}(n)2​ Wess-Zumino-Witten model and U(2n)(2n)(2n)/Sp(n)(n)(n) nonlinear sigma model.
Abstract In this paper we investigate certain fusion relations associated to an integrable vertex model on the square lattice which is invariant under Sp (4) symmetry. We establish a set of functional relations which include a transfer matrix inversion identity. The solution of these relations in the thermodynamic limit allows us to compute the partition function per site of the fundamental Sp (4) representation of the vertex model. As a byproduct we also obtain the partition function per site of a vertex model mixing the four and five dimensional representations of the Sp (4) symmetry.
The multichannel Kondo model exhibits non-Fermi-liquid behavior in the overscreened case, when the number of channels, k, is greater than twice the size of the impurity spin, s. We show that, for overscreening, exchange anisotropy is irrelevant at the low-temperature fixed point for s=1/2 or s=k/2-1/2, but relevant for all other values of s. However, an external field or channel asymmetry is relevant, producing crossover to Fermi-liquid fixed points with different phase shifts for each spin in the first case and for each channel in the second. These results are elucidated by explicit comparison of analytic finite-size spectra derived from conformal field theory with those obtained from numerical renormalization-group calculations. The relevance of the results (for k=2 and s=1/2) to the quadrupolar Kondo Hamiltonian (which has been proposed as a model for many uranium-based heavy-fermion materials) will be briefly discussed. Also, a larger, a/Isymplectic symmetry Sp(2k) is shown to be present in the k-channel Kondo model.