The Luther-Emery liquid: Spin gap and anomalous flux period

TL;DR

This paper demonstrates that in the Luther-Emery liquid with a spin gap, the ground state energy exhibits an exact $hc/2e$ flux period, with finite size effects diminishing exponentially, contrasting with the spin gapless case.

Contribution

It provides an exact analysis of flux periodicity in the Luther-Emery liquid using finite size bosonization, highlighting the role of the spin gap.

Findings

Ground state energy has an exact $hc/2e$ flux period in systems with a spin gap.

Finite size corrections decay exponentially with system size.

Contrasts behavior with spin gapless systems for both even and odd particle numbers.

Abstract

We study the dependence of the ground state energy on an applied Aharonov-Bohm flux $\Phi$ for the Luttinger model with large momentum scattering. Employing the method of finite size bosonization, we show that for systems with a spin gap but with gapless charge degrees of freedom, the ground state energy has an exact period of $hc/2e$, i. e. {\em half} a flux quantum, in the limit of large system size $L$. Finite size corrections are found to vanish exponentially in $L$. This behavior is contrasted to that of the spin gapless case, for both even and odd particle number. Generalizations to finite temperature are also discussed.