The N-Leg spin-S Heisenberg ladders: A DMRG study

We investigate the N-leg spin-S Heisenberg Ladders by using the density matrix renormalization group method. We present estimates of the spin gap ${\mathrm{\Delta }}_s$ and of the ground state energy per site $e_{\mathrm{\infty }}^N$ in the thermodynamic limit for ladders with widths up to six legs and spin $S\le \frac{5}{2}$. We also estimate the ground state energy per site $e_{\mathrm{\infty }}^{2D}$ for the infinite two-dimensional spin-S Heisenberg model. Our results support that for ladders with semi-integer spins the spin excitation is gapless for $N$ odd and gapped for N even. Whereas for integer spin ladders the spin gap is nonzero, independent of the number of legs. Those results agree with the well known conjectures of Haldane and S'en'echal-Sierra for chains and ladders, respectively. We also observe edge states for ladders with $N$ odd, similar to what happens in the integer spin chains.