An improved method for computing correlation functions of one-dimensional fermion systems

Correlation functions of one-dimensional Tomonaga-Luttinger models with sine-Gordon-like extensions are computed using bosonisation and scaling techniques. The author shows that by expanding the full correlation functions instead of considering only their first cumulants, exponents for their asymptotic decay, logarithmic corrections as well as renormalised amplitudes can be obtained. Applied to the Hubbard model, the method produces for the first time correlation functions consistent with its symmetries, exact spectrum and numerical simulations.