Determination of Tomonaga-Luttinger parameters for a two-component liquid

TL;DR

This paper maps critical spin-1 chains, including SU(3) models, to free boson theories, and numerically determines Tomonaga-Luttinger parameters by analyzing scaling dimensions via exact diagonalization and DMRG.

Contribution

It provides a method to extract Tomonaga-Luttinger parameters for two-component liquids from lattice models using numerical techniques.

Findings

Successfully mapped spin-1 chains to free boson theories

Derived analytic formulas for scaling dimensions in terms of Luttinger parameters

Numerically tracked the evolution of parameters with lattice model variations

Abstract

We provide evidence for the mapping of critical spin-1 chains, in particular the SU(3) symmetric bilinear-biquadratic model with additional interactions, to free boson theories using exact diagonalization and the density matrix renormalization group algorithm. Using the correspondence with a conformal field theory with central charge c=2, we determine the analytic formulae for the scaling dimensions in terms of four Tomonaga-Luttinger liquid parameters. By matching the lowest scaling dimensions, we numerically calculate these field-theoretic parameters and track their evolution as a function of the parameters of the lattice model.