Twisted boundary conditions and the adiabatic ground state for the attractive XXZ Luttinger liquid.

Abstract

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 \ensuremath{\Delta}=cos(\ensuremath{\pi}/p) with p noninteger, the adiabatic ground state is periodic in the magnetic flux threading the chain, with period two 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 rapidly around to the other Fermi point where it sequentially unbinds. We find Berry's phase for the whole process to be [p]\ensuremath{\pi}. For p integer, as \ensuremath{\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. The charge-carrying mass of the fermions is calculated by finding the energy of the adiabatic ground state with twisted boundary conditions.