Hetero-junction of two quantum wires: Critical line and duality

초록

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

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