Phase Operator and Lattice Green’s Function for Ring-Lattice Model in p-th Nearest Neighbour Interact ion Approximation

In dealing with the one-dimensional lattice model, we replace the traditionally needed Born-Von-Karmann periodic boundary condition with two additional Hamiltonian terms to make up a ring-lattice. In so doing, a unitary phase operator and the corresponding Hermite phase angle operator can be introduced as those in quantum optics theory. The new Hamiltonian is invariant under the phase shift transformation. Moreover, the lattice Green’s function in the p-th nearest interaction approximation can also be easily derived from the new Hamiltonian. which becomes the well-known lattice Green’s function when the ring is infinite.