Infinite boundary conditions as a current source for impurity conductance in a quantum wire

Developing nanoelectronic devices requires a detailed understanding of conduction in quantum wires. Numerical methods based on the density matrix renormalization group (DRMG) are excellent tools for studying one-dimensional quantum systems, but studying finite biases and currents requires time-dependent simulations, which remain challenging. Here we consider the problem of conductance across an impurity (or quantum dot) connected to metallic leads. Previous studies^1,2 have used a finite wire with open boundary conditions, which suffers from strong finite-size effects. We use a powerful numerical method incorporating infinite boundary conditions³ (obtained from infinite DMRG⁴) to simulate semi-infinite leads. We extract linear conductance from static correlation functions within a finite-size window that contains the impurity. Building on that, we use a time-dependent method to extract conductance in the presence of finite bias.
¹ K.A. Al-Assanieh et al. Phys. Rev. B 73, 195304 (2006)
² Dias da Silva et al. Phys. Rev. B 78, 195317 (2008)
³ H.N. Pien, G. Vidal & I.P. McCulloch, Phys. Rev. B 86, 245107 (2012)
⁴ C.Y. Lo, Y. Fukusumi, M. Oshikawa, Y.J. Kao & P.C. Chen, arXiv:1805.05006