Quantum impurity in a Tomonaga-Luttinger liquid: continuous-time quantum Monte Carlo approach

Abstract

We develop a continuous-time quantum Monte Carlo (CTQMC) method for quantum impurities coupled to interacting quantum wires described by a Tomonaga-Luttinger liquid. The method is negative-sign free for any values of the Tomonaga-Luttinger parameter, which is rigorously proved, and thus, efficient low-temperature calculations are possible. Duality between electrons and bosons in one dimensional systems allows us to construct a simple formula for the CTQMC algorithm in these systems. We show that the CTQMC for Tomonaga-Luttinger liquids can be implemented with only minor modifications of previous CTQMC codes developed for impurities coupled to non-interacting fermions. We apply this method to the Kane-Fisher model of a potential scatterer in a spin-less quantum wire and to a single spin coupled with the edge state of a two-dimensional topological insulator assuming an anisotropic XXZ coupling. Various dynamical response functions such as the electron Green's function and spin-spin correlation functions are calculated numerically and their scaling properties are discussed.

15 pages, 11 figures

References in corpus (11)

• Continuous-time Monte Carlo methods for quantum impurity models
• The Helical Liquid and the Edge of Quantum Spin Hall Systems
• Kondo effect in the helical edge liquid of the quantum spin Hall state
• Topological Kondo effect with Majorana fermions
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• Renormalization group approach for the scattering off a single Rashba impurity in a helical liquid
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• Numerical study of transport through a single impurity in a spinful Tomonaga-Luttinger liquid