The end of c=1 CFT

TL;DR

This paper investigates the instability of the c=1 conformal field theory, particularly its transition to a ferromagnetic state, revealing how key parameters behave near the critical point.

Contribution

It provides a detailed analysis of the instability mechanism of c=1 CFT models, especially the transition to ferromagnetism, and characterizes the behavior of spin wave velocity and critical dimension.

Findings

Spin wave velocity $v$ and $1/K$ scale as $ oot{\Delta_c - \Delta}$ near criticality.

The study clarifies the conditions under which c=1 CFT becomes unstable.

It links the instability to physical transitions in 1D quantum systems.

Abstract

Conformal field theory (CFT) with the central charge c=1 is important both in the field theory and in the condensed matter physics, since it has the continuous internal symmetry (U(1) or SU(2)) and a marginal operator, and it is an effective theory of many 1D quantum spin and 1D electron systems. So it is valuable to understand how the c=1 CFT models become unstable. In this paper we discuss an instability of the c=1 CFT, that is, the transition to the ferromagnetic state. For the U(1) CFT case, we find that the spin wave velocity $v$ and the critical dimension $K$ behave $v, 1/K \propto \sqrt{\Delta_c -\Delta}$ under reasonable assumptions.