Numerical Solution of the spin-1/2 Heisenberg Antiferromagnetic Chains Using a Projector Method

An efficient projector method is proposed to calculate the energy gap between the ground,state and the first excited state of the spin-1/2 Heisenberg antiferromagnetic chains. We exactly computed the two lowest-lying energies for the magnetization S_t^z= 0 and the lowestlying energy for S_t^z=±1 on chains up to 16 spins. The lowest-lying energy stat6 for S_t^z= 0 is a singlet ground state. The second lowest-lying energy state for S_t^z= 0 and the lowestlying energy states for S_t^z=±1 are triplet degenerate, which are the first excited energy states. We also imposed the Monte Carlo technique to estimate the lowest-lying energies for both S_t^z= 0 and 1 on longer chains up to 32 spins. We found that the singlet-triplet energy gap trends to zero as N→∞.