The excitation spectrum of 1d spinless Bose-gas (schematically) Fig.2 The spectrum of the same system in a finite volume Fig.3 The lattice system in the uniform magnetic field
- Zabrodin A.V, Ovchinnikov A.A. Teor.Mat.Fiz
Using the finite-size effects the scaling dimensions and correlation functions of the main operators in continuous and lattice models of 1d spinless Bose-gas with pairwise interaction of rather general form are obtained. The long-wave properties of these systems can be described by the Gaussian model with central charge c = 1. The disorder operators of the extended Gaussian model are found to correspond to some non-local operators in the XXZ Heisenberg antiferromagnet. Just the same approach is applicable to fermionic systems. Scaling dimensions of operators and correlation functions in the systems of interacting Fermi-particles are obtained. We present a universal treatment for 1d systems of different kinds which is independent of the exact integrability and gives universal expressions for critical exponents through the thermodynamic characteristics of the system.