Embedding method for the scattering phase in strongly correlated quantum dots

Abstract

Abstract. The embedding method for the calculation of the conductance through interacting systems connected to single channel leads is generalized to obtain the full complex transmission amplitude that completely characterizes the effective scattering matrix of the system at the Fermi energy. We calculate the transmission amplitude as a function of the gate potential for simple diamond-shaped lattice models of quantum dots with nearest neighbor interactions. In our simple models we do not generally observe an interaction dependent change in the number of zeroes or phase lapses that depend only on the symmetry properties of the underlying lattice. Strong correlations separate and reduce the widths of the resonant peaks while preserving the qualitative properites of the scattering phase.

Mesoscopic behavior of the transmission phase through confined correlated electronic systems

“…In this appendix we reformulate the embedding approach for the transmission phase put forward in Ref. 40 , settling the notation and the basis of the numerical method used in Secs. III and IV.…”

“…This procedure is numerically demanding, and constitutes the bottleneck of the embedding method. 37,38,40,[45][46][47][48] The eigenphases of the scattering matrix are, for cos θ cos ξ > 0, ϕ 1 = ζ + Arcsin(cos θ cos ξ) and ϕ 2 = ζ + π − Arcsin(cos θ cos ξ), and the corresponding Wigner time is…”

“…3). When the single-particle level-spacing is of the order of the level-width (∆ Γ), the transmission zeros with U = 0 typically exhibit the same qualitative behavior as in the non-interacting case U = 0 [29,40]. This situation typically happens in small systems when t D = 1.…”

“…This situation typically happens in small systems when t D = 1. For instance, in the case with M = 4 and on-site energies chosen such that one has a transmission zero at U = 0, the effect of the interactions is to separate the peaks, reducing their widths without changing the qualitative behavior of the scattering phase 40 .…”

“…11,12,30 We use the DMRG-based embedding method to extract the transmission properties of the system [37][38][39] and its recent extension to calculate the transmission phase. 40 We review such an approach in Appendix A and illustrate its power for a one-dimensional interacting quantum wire, including a numerical verification of the Friedel sum rule in Appendix B.…”