The Asymptotics of the Correlations Functions in $(1+1)d$ Quantum Field Theory From Finite Size Effects in Conformal Theories

TL;DR

This paper derives the asymptotic behavior of correlation functions in 1+1 dimensional quantum field theories using finite-size effects, providing universal expressions for critical exponents across various models.

Contribution

It introduces a universal approach to compute correlation functions and scaling dimensions in 1d quantum systems, independent of integrability.

Findings

Correlation functions expressed via finite-size effects.

Universal formulas for critical exponents.

Application to both bosonic and fermionic systems.

Abstract

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 {\it 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.