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We study numerically the universal conductance of Luttinger liquids wire witha single impurity via the Muti-scale Entanglement Renormalization Ansatz(MERA). The scale invariant MERA provides an efficient way to extract scalingoperators and scaling dimensions for both the bulk and the boundary conformalfield theories. By utilizing the key relationship between the conductancetensor and ground-state correlation function, the universal conductance can beevaluated within the framework of the boundary MERA. We construct the boundaryMERA to compute the correlation functions and scaling dimensions for theKane-Fisher fixed points by modeling the single impurity as a junction (weaklink) of two interacting wires. We show that the universal behavior of thejunction can be easily identified within the MERA and argue that the boundaryMERA framework has tremendous potential to classify the fixed points in generalmulti-wire junctions.

Quantum Impurity in Luttinger Liquid: Universal Conductance with Entanglement Renormalization