Dresden 2017 – scientific programme

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TT: Fachverband Tiefe Temperaturen

TT 24: Low-Dimensional Systems: 1D - Theory

TT 24.8: Talk

Tuesday, March 21, 2017, 11:30–11:45, HSZ 204

DMRG method for the conductance of one-dimensional correlated systems — •Jan Bischoff — Leibniz Universität Hannover

We present an accurate and efficient procedure for computing the zero-temperature linear conductance of correlated one-dimensional systems using the density-matrix renormalization group (DMRG). Building on [1], we express the conductance within the linear response theory as the limits of dynamical correlation functions for finite systems. These correlation functions can be calculated with the dynamical DMRG algorithm. We have first studied non-interacting models to determine an appropriate scaling of frequency, system size, and spectral broadening by comparison with exact results. The method is demonstrated for interacting systems using the one-dimensional spinless fermion model. Our results for this lattice model agree with the field-theoretical predictions for the renormalization of the conductance in a pure Luttinger liquid as well as for the effects of an impurity in a Luttinger liquid [2]. We have found that this new approach is more efficient than a simulation of the nonequilibrium transport [3] in the linear response regime. We have also tested our approach on the Hubbard model and we plan to extend it to the problem of an interacting quantum wire connected to two broad and weakly-interacting leads.

[1] D. Bohr, P. Schmitteckert, and P.W. Wölfle, Europhys. Lett., 73, 246 (2006)

[2] C.L. Kane and M.P.A. Fisher, PRB 46, 15233 (1992)

[3] M. Einhellinger, A. Cojuhovschi, and E. Jeckelmann, Phys. Rev. B 85, 235141 (2012)