Universal Scaling of the Quantum Conductance of an Inversion-Symmetric Interacting Model

We consider quantum transport of spinless fermions in a one-dimensional (1D) lattice embedding an interacting region (two sites with intersite repulsion U and intersite hopping t(d), coupled to leads by hopping terms t(c)). Using the numerical renormalization group for the particle-hole symmetric case, we study the quantum conductance g as a function of the intersite hopping td. The interacting region, which is perfectly reflecting when t(d) -> 0 or t(d) ->(infinity), becomes perfectly transmitting if td takes an intermediate value tau(U, t(c)), which defines the characteristic energy of this interacting model. When t(d) < t(c) < root U, g is given by a universal function of the dimensionless ratio X=t(d)/tau. This universality characterizes the noninteracting regime where tau=t(c)(2), the perturbative regime (Ut(c)(2)) where tau is twice the characteristic temperature TK of an orbital Kondo effect induced by the inversion symmetry. When t(d) < tau, the expression g (X) = 4(X+X(-1))(-2) valid without interaction describes also the conductance in the presence of the interaction. To obtain those results, we map this spinless model onto an Anderson model with spins, where the quantum impurity is at the end point of a semi-infinite 1D lead and where td plays the role of a magnetic field h. This allows us to describe g (t(d)) using exact results obtained for the magnetization m (h) of the Anderson model at zero temperature. We expect this universal scaling to be valid also in models with two-dimensional (2D) leads, and observable using 2D semiconductor heterostructures and an interacting region made of two identical quantum dots with strong capacitive interdot coupling and connected via a tunable quantum point contact.