Conformal field theory in Tomonaga-Luttinger model with $1/r^\beta$ type long-range interactions

TL;DR

This paper investigates how conformal field theory applies to the Tomonaga-Luttinger model with long-range $1/r^eta$ interactions, revealing deviations in the effective central charge and validating predictions through numerical tests.

Contribution

It demonstrates the validity of CFT in long-range interacting systems and uncovers deviations in the effective central charge due to long-range interactions.

Findings

Finite size corrections depend on the power of long-range interactions.

Effective central charge deviates from 1 in the presence of long-range interactions.

Numerical tests confirm the conformal predictions for excitations and ground state.

Abstract

The validity of the CFT in the Tomonaga-Luttinger liquid with the $1/r^\beta$ type long-range interactions is discussed. The arguments by CFT for long-range forward scatterings predict the finite size corrections which depend on the power of the long-range interactions. Especially from finite size corrections in the ground state, we find the effective central charge deviates from $c=1$. These conformal arguments are numerically tested in the one particle excitations and the ground state.