Asymmetric spin-1/2 two-leg ladders: Analytical studies supported by exact diagonalization, DMRG, and Monte Carlo simulations

作者：Aristov D N^*; Bruenger C; Assaad F F; Kiselev M N; Weichselbaum A; Capponi S; Alet F

来源：Physical Review B, 2010, 82(17): 174410.

DOI：10.1103/PhysRevB.82.174410

We consider asymmetric spin-1/2 two-leg ladders with nonequal antiferromagnetic (AF) couplings J(parallel to) and kappa J(parallel to) along legs (kappa <= 1) and ferromagnetic rung coupling, J(perpendicular to). This model is characterized by a gap Delta in the spectrum of spin excitations. We show that in the large J(perpendicular to) limit this gap is equivalent to the Haldane gap for the AF spin-1 chain, irrespective of the asymmetry of the ladder. The behavior of the gap at small rung coupling falls in two different universality classes. The first class, which is best understood from the case of the conventional symmetric ladder at kappa = 1, admits a linear scaling for the spin gap Delta similar to J(perpendicular to). The second class appears for a strong asymmetry of the coupling along legs, kappa J(parallel to) << J(perpendicular to) << J(parallel to) and is characterized by two energy scales: the exponentially small spin gap Delta similar to J(perpendicular to) exp(-J(parallel to)/J(perpendicular to)), and the bandwidth of the low-lying excitations induced by a Suhl-Nakamura indirect exchange similar to J(perpendicular to)(2)/J(parallel to). We report numerical results obtained by exact diagonalization, density-matrix renormalization group and quantum Monte Carlo simulations for the spin gap and various spin correlation functions. Our data indicate that the behavior of the string order parameter, characterizing the hidden AF order in Haldane phase, is different in the limiting cases of weak and strong asymmetries. On the basis of the numerical data, we propose a low-energy theory of effective spin-1 variables, pertaining to large blocks on a decimated lattice.

• 出版日期2010-11-8