Quantum Impurity in Luttinger Liquid: Universal Conductance with Entanglement Renormalization

Abstract

We study numerically the universal conductance of Luttinger liquids wire with a single impurity via the Muti-scale Entanglement Renormalization Ansatz (MERA). The scale invariant MERA provides an efficient way to extract scaling operators and scaling dimensions for both the bulk and the boundary conformal field theories. By utilizing the key relationship between the conductance tensor and ground-state correlation function, the universal conductance can be evaluated within the framework of the boundary MERA. We construct the boundary MERA to compute the correlation functions and scaling dimensions for the Kane-Fisher fixed points by modeling the single impurity as a junction (weak link) of two interacting wires. We show that the universal behavior of the junction can be easily identified within the MERA and argue that the boundary MERA framework has tremendous potential to classify the fixed points in general multi-wire junctions.

14 pages, 18 figures

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Cited by in corpus (6)

• Tensor network renormalization yields the multi-scale entanglement renormalization ansatz
• Algorithms for tensor network renormalization
• Entanglement renormalization and wavelets
• Circuit Quantum Simulation of a Tomonaga-Luttinger Liquid with an Impurity
• Representation and design of wavelets using unitary circuits
• Crossover of Correlation Functions near a Quantum Impurity in a Tomonaga-Luttinger Liquid