N-leg spin-SHeisenberg ladders: A density-matrix renormalization group study

Abstract

We investigate the $N$-leg spin-$S$ Heisenberg ladders by using the density matrix renormalization group method. We present estimates of the spin gap ${$\Delta${}}_{s}$ and of the ground-state energy per site ${e}_{$\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 ${e}_{$\infty${}}^{2\mathrm{D}}$ 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 spin chains.