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Sabine Andergassen Max-Planck-Institut für Festkörperforschung, Heisenbergstr. 1, 70569 Stuttgart, Germany |
Using a functional renormalization group and DMRG, we compute the flow of the renormalized impurity potential for a single impurity in a Luttinger liquid over the entire energy range from the microscopic scale of a lattice-fermion model down to the low-energy limit. The nonperturbative method provides a complete real-space picture of the effective impurity potential. We confirm the universality of the open chain fixed point, but it turns out that very large systems (10^4 -10^5 sites) are required to reach the fixed point for realistic choices of the impurity and interaction parameters. [1] This also holds for the persistent current in an interacting ring with an impurity threaded by a magnetic flux. [2]
[1] V. Meden, W. Metzner, U. Schollwöck, and K. Schönhammer, Phys. Rev. B 65, 045318 (2002); J. of Low Temp. Phys. 126, 1147 (2002).
[2] V. Meden and U. Schollwöck, Phys. Rev. B 67, 035106 (2003) .