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

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.