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

We consider quantum transport of spinless fermions in a 1D lattice embedding an interacting region (two sites with inter-site repulsion U and inter-site hopping td, coupled to leads by hopping terms tc). Using the numerical renormalization group for the particle-hole symmetric case, we study the quantum conductance g as a function of the inter-site hopping td. The interacting region, which is perfectly reflecting when td -> 0 or td -> infinity, becomes perfectly transmitting if td takes an intermediate value τ(U,tc) which defines the characteristic energy of this interacting model. When td < tc sqrt(U), g is given by a universal function of the dimensionless ratio X=td/τ. This universality characterizes the non-interacting regime where τ=tc^2, the perturbative regime (U < tc^2) where τcan be obtained using Hartree-Fock theory, and the non-perturbative regime (U > tc^2) where τis twice the characteristic temperature TK of an orbital Kondo effect induced by the inversion symmetry. When td < τ, the expression g(X)=4/(X+1/X)^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(td) 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 2D leads, and observable using 2D semi-conductor heterostructures and an interacting region made of two identical quantum dots with strong capacitive inter-dot coupling and connected via a tunable quantum point contact.