Exact solution of the Heisenberg XX model with twisted boundary conditions

Abstract

We develop a method to solve the Heisenberg XX model in a transverse field with twisted boundary conditions. We investigate the twist effects on the ground state for the different external magnetic fields. The results indicate that the boundary energy is symmetric under the reflection of θ=π and obeys a scaling behavior. The properties of the ground state strongly depend on the coupling between the particle number operator and the twist angle. The twist effects can be controlled by the external magnetic field only when the system is in the magnetic order phase. We also calculate the specific heat and the nearest neighbor entanglement of the boundary sites, and find the behaviors of the boundary sites are sensitive to the twist angle. The boundary sites exhibit different behaviors compared with the normal sites with the variation of twist angle, which can be tuned by the external magnetic field.