Twisted Boundary Conditions and the Adiabatic Ground State for the   Attractive XXZ Luttinger Liquid
  The one-dimensional attractive lattice fermion gas equivalent to the Heisenberg-Ising spin 1/2 chain is studied for a ring geometry threaded by magnetic flux. We find that for charged fermions having interaction strength $\Delta=\cos(\pi / p)$ with $p$ {\it noninteger}, the adiabatic ground state is periodic in the magnetic flux threading the chain, with period 2 flux quanta, as found by Shastry and Sutherland for the repulsive case. We find that, at particular values of the threading field, a sequence of initially zero-energy bound states form at the Fermi surface during the adiabatic process, the largest containing $[p]$ (the integer part of $p$) fermions. This largest bound state moves around to the other Fermi point and sequentially unbinds. We find Berry's Phase for the whole process to be $[p] \pi$. For $p$ {\it integer}, as $\Phi$ increases, eventually all the particles in the system go into bound states of size $[p]$. The period in this case is of order the size of the system. 
Naichang Yu and Michael Fowler