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

2015/02/28 by Olabode M. Sule, Olabode Mayodele Sule, Hitesh J. Changlani +2 · 12 citations
Mathematics · Physics and Astronomy · #Bilinear interpolation #Boson #Central charge #Conformal field theory #Conformal map #Lattice (music) #Luttinger liquid #Mathematical analysis #Mathematical physics #Mathematics #Mean field theory #Physics #Physics of Superconductivity and Magnetism #Quantum Chromodynamics and Particle Interactions #Quantum many-body systems #Quantum mechanics #Renormalization group #Scaling #Statistical physics #cond-mat.str-el

paper · pdf · doi:10.1103/physrevb.92.075128

published in Physical Review B 92(7) (American Physical Society) · 11 pages, 10 figures. The first two authors contributed equally to this work. Introduction updated, several referee comments incorporated

openalex publication_date 2015/08/18 · arxiv created 2016/01/28 · arxiv updated 2016/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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 formulas 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.

Citations

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• String Theory and M-Theory
• Conformal Field Theory