Existence of Low-Temperature Critical Regime in 1D Luttinger Liquid with a Weak Link

TL;DR

This paper investigates the boundary sine-Gordon model's low-temperature behavior, revealing a critical regime in 1D Luttinger liquids with a weak link, and connects it to the Kondo model universality class.

Contribution

It provides an exact solution for the boundary sine-Gordon model in a specific scaling dimension range, identifying a low-temperature critical regime in 1D Luttinger liquids with a weak link.

Findings

Infrared fixed point for Δ > 2/3 belongs to the underscreened anisotropic Kondo model

Boundary specific heat scales as C ∼ T^{2/Δ - 2} at low temperatures

Existence of a low-temperature critical regime in 1D Luttinger liquids with a weak link

Abstract

The exact solution of the boundary sine-Gordon model is studied in the region where the scaling dimension of the boundary field $1 < \Delta < 1$. It is shown that at $\Delta > 2/3$ the infrared fixed point belongs to the universality class of the underscreened anisotropic Kondo model. The boundary contribution to the specific heat scales as $C \sim T^{2\Delta^{-1} - 2}$ at small temperatures.