Microscopic approach to a class of 1D quantum critical models

TL;DR

This paper demonstrates how the $c=1$ free boson conformal field theory effectively describes the large-distance behavior of correlation functions in a broad class of 1D quantum critical models, starting from microscopic principles.

Contribution

It provides a microscopic derivation of the emergence of the free boson CFT as an effective theory for 1D quantum critical models using finite volume form factors.

Findings

Shows the emergence of $c=1$ free boson CFT in 1D quantum critical models

Establishes a correspondence between local operators and vertex operators of the free boson model

Provides a microscopic derivation from finite volume matrix elements

Abstract

Starting from the finite volume form factors of local operators, we show how and under which hypothesis the $c=1$ free boson conformal field theory in two-dimensions emerges as an effective theory governing the large-distance regime of multi-point correlation functions in a large class of one dimensional massless quantum Hamiltonians. In our approach, in the large-distance critical regime, the local operators of the initial model are represented by well suited vertex operators associated to the free boson model. This provides an effective field theoretic description of the large distance behaviour of correlation functions in 1D quantum critical models. We develop this description starting from the first principles and directly at the microscopic level, namely in terms of the properties of the finite volume matrix elements of local operators.