Crossover of Correlation Functions near a Quantum Impurity in a Tomonaga-Luttinger Liquid

TL;DR

This paper introduces a numerical method using infinite DMRG to accurately compute the crossover of correlation functions near a quantum impurity in a Tomonaga-Luttinger liquid, confirming field-theory predictions.

Contribution

Develops a novel infinite DMRG-based numerical approach to calculate the full crossover of correlation functions near impurities in Luttinger liquids.

Findings

Successfully computes the entire crossover of correlation functions.

Results agree with field-theory predictions.

Method applicable to other impurity problems in quantum liquids.

Abstract

An impurity in a Tomonaga-Luttinger liquid leads to a crossover between short- and long-distance regime which describes many physical phenomena. However, calculation of the entire crossover of correlation functions over different length scales has been difficult. We develop a powerful numerical method based on infinite DMRG utilizing a finite system with infinite boundary conditions, which can be applied to correlation functions near an impurity. For the $S=1/2$ chain, we demonstrate that the full crossover can be precisely obtained, and that their limiting behaviors show a good agreement with field-theory predictions.