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

We study the dependence of the ground state energy on an applied Aharonov-Bohm flux Φ 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., 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.