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Hetero-Junction of Two Quantum Wires: Critical Line and Duality

Applying the Fermi-Bose equivalence and the boundary state formulation, we study the hetero-junction of two quantum wires. Two quantum wires are described by Tomonaga-Luttinger (TL) liquids with different TL parameters and electrons transport between two wires is depicted by a simple hopping interaction. We calculate the radiative corrections to the hopping interaction and obtain the renormalization (RG) exponent, making use of the perturbation theory based on the boundary state formulation. The model exhibits a phase transition at zero temperature. We discuss the critical line which defines the phase boundary on the two dimensional parameter space. The model also exhibits the particle-kink duality, which maps the strong coupling regime of the model onto the weak coupling regime of the dual model. The strong coupling regime of the model is found to match exactly the weak coupling regime of the dual model. This model is also important to study the critical behaviors of the two dimensional dissipative system with anisotropic friction coefficients.