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

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.

11 pages, 10 figures. The first two authors contributed equally to this work. Introduction updated, several referee comments incorporated

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• Anomalies and unnatural stability of multi-component Luttinger liquids in ${\mathbb{Z}}_n\times {\mathbb{Z}}_n$ spin chains
• Multimagnon dynamics and thermalization in the $S=1$ easy-axis ferromagnetic chain
• Parent Hamiltonians for lattice Halperin states from free-boson conformal field theories
• Statistics-tuned phases of pseudofermions in one dimension
• Waveguide QED toolboxes for universal quantum matter
• The dynamical structure factor of the SU(3) Heisenberg chain: The variational Monte Carlo approach