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Tunneling in quantum wires: Exact solution of the spin isotropic case

1997; American Physical Society; Volume: 56; Issue: 12 Linguagem: Inglês

10.1103/physrevb.56.7598

1095-3795

Frédéric Lesage, Hubert Saleur, P. Simonetti,

Quantum many-body systems

We show that the problem of impurity tunneling in a Luttinger liquid of electrons with spin is solvable in the spin isotropic case ($g_\sigma=2$, $g_\rho$ arbitrary). The resulting integrable model is similar to a two channel anisotropic Kondo model, but with the impurity spin in a "cyclic representation" of the quantum algebra $su(2)_q$ associated with the anisotropy. Using exact, non-perturbative techniques we study the RG flow, and compute the DC conductance. As expected from the analysis of Kane and Fisher we find that the IR fixed point corresponds to two separate leads. We also prove an exact duality between the UV and IR expansions of the current at vanishing temperature.