Verification of Haldane Conjecture for Lower Spins via Density Matrix Renormalization Group

The Haldane conjecture states that Heisenberg spin chain with half-integer spins are gapless, while those with integer spins are gapped. Using Density Matrix Renormalization Group, we verified the Haldane conjecture for lower spins by calculating the energy level differences, analyzing the scaling behavior of the entanglement entropy with system size, and examining the decay of the spin-spin correlation function.