Compounds such as vanadyl pirophosphate (VO2)P2O7 and some cuprate systems (example: SrCu2O3 and Sr2Cu3O5) are experimental realizations of the Heisenberg ladders. These compounds are well known examples of strongly correlated systems. The physics of these systems is described, correctly, only by non-perturbative methods. In this work, we investigate the spin-S N-leg Heisenberg ladders using the density matrix renormalization group (DMRG) technique. We obtain estimates of the ground state energy per site, in thermodynamic limit (e∞), as well as of the spin gap (ΔS) for the ladders with spin up to S = 5/2 . We found that for half-integer spin ladders the spin gap is zero (finite) for N odd (even); whereas for the integer spin ladders our results support a finite spin gap, independent of the number of legs. These results are in agreement with the Haldane-Sierra s conjecture [1 3]. We also estimate the value of e∞ for the two-dimensional spin-S Heisenberg model from the ground state energies, in the thermodynamic limit, of the Heisenberg ladders.
The goal of this project is to study the ground-state properties of frustrated spin-1/2 two- and three-leg Heisenberg ladders, and to investigate possible effects of diagonal couplings on spin gaps. The ground-state and the first-excited-state energies of these two systems are calculated systematically by using the density matrix renormalization group method. The ground state phase diagrams for these two systems are obtained. For the frustrated two-leg ladder, we found that the spin gap is insensitive to the change of the FM diagonal coupling constant. This is in agreement with experimental suggestions. For the frustrated three-leg ladder, we conclusively proved that introducing AF diagonal couplings can not change the gapless property of the ground state.
We consider a two-leg ladder system with interactions varying from constant rung coupling to systematic diminishing of rung interactions leading to diverging chains. We compare and contrast their ground state and excitation characteristics using density matrix renormalization group methods. We find that the finite spin gap in a constant coupling ladder develops into a gapless excitation with slight diminishing of the distance dependent coupling. Varying the spatial range of the rung coupling, we derive the effective length scale of triplet excitations in these ladder classes of systems.
We consider asymmetric spin-
21 two-leg ladders with nonequal antiferromagnetic (AF) couplings ${J}_{\ensuremath{\parallel}}$ and $\ensuremath{\kappa}{J}_{\ensuremath{\parallel}}$ along legs $(\ensuremath{\kappa}\ensuremath{\le}1)$ and ferromagnetic rung coupling, ${J}_{\ensuremath{\perp}}$. This model is characterized by a gap $\ensuremath{\Delta}$ in the spectrum of spin excitations. We show that in the large ${J}_{\ensuremath{\perp}}$ 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 $\ensuremath{\kappa}=1$, admits a linear scaling for the spin gap $\ensuremath{\Delta}\ensuremath{\sim}{J}_{\ensuremath{\perp}}$. The second class appears for a strong asymmetry of the coupling along legs, $\ensuremath{\kappa}{J}_{\ensuremath{\parallel}}⪡{J}_{\ensuremath{\perp}}⪡{J}_{\ensuremath{\parallel}}$ and is characterized by two energy scales: the exponentially small spin gap $\ensuremath{\Delta}\ensuremath{\sim}{J}_{\ensuremath{\perp}}\text{ }\text{exp}(\ensuremath{-}{J}_{\ensuremath{\parallel}}/{J}_{\ensuremath{\perp}})$, and the bandwidth of the low-lying excitations induced by a Suhl-Nakamura indirect exchange $\ensuremath{\sim}{J}_{\ensuremath{\perp}}^{2}/{J}_{\ensuremath{\parallel}}$. 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.
We study the ground state and low-lying excited states of the Kitaev-Heisenberg model on a two-leg ladder geometry using the density-matrix renormalization-group and Lanczos exact diagonalization methods. The Kitaev and Heisenberg interactions are parametrized as $K=sin\ensuremath{\phi}$ and $J=cos\ensuremath{\phi}$ with an angle parameter $\ensuremath{\phi}$. Based on the results for several types of order parameters, excitation gaps, string order parameter, and entanglement spectra, the $\ensuremath{\phi}$-dependent ground state phase diagram is determined. Remarkably, the phase diagram is quite similar to that of the Kitaev-Heisenberg model on a honeycomb lattice, exhibiting the same long-range-ordered states, namely rung singlet (analog to N\'eel in three dimensions), zigzag, ferromagnetic, and stripy, and the presence of gapped spin liquids around the exactly solvable Kitaev points $\ensuremath{\phi}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2$. We also calculate the expectation value of a plaquette operator corresponding to a $\ensuremath{\pi}$-flux state in order to establish how the gapped Kitaev spin liquid extends away from the $\ensuremath{\phi}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2$. Furthermore, we determine the dynamical spin structure factor and discuss the effect of the Kitaev interaction on the spin-triplet dispersion.
Motivated by the recent experiment on
K2Cu3O(SO4)3, an edge-shared tetrahedral spin-cluster compound [M. Fujihala, T. Sugimoto, T. Tohyama, S. Mitsuda, R. A. Mole, D. H. Yu, S. Yano, Y. Inagaki, H. Morodomi, T. Kawae, H. Sagayama, R. Kumai, Y. Murakami, K. Tomiyasu, A. Matsuo, and K. Kindo, Phys. Rev. Lett. 120, 077201 (2018)], we investigate two-leg spin-cluster ladders with the plaquette number
np in each cluster up to 6 by the density-matrix renormalization-group method. We find that the phase diagrams of such ladders strongly depend on the parity of
np. For even
np, the phase diagrams have two phases; one is the Haldane phase, and the other is the cluster rung-singlet phase. For odd
np, there are four phases, which are a cluster-singlet phase, a cluster rung-singlet phase, a Haldane phase, and an even Haldane phase. Moreover, in the latter case the region of the Haldane phase increases while that of the cluster-singlet phase and the even Haldane phase shrinks as
np increases. We thus conjecture that in the large
np limit the phase diagrams will become independent of
np. By analyzing the ground-state energy and entanglement entropy we obtain the order of the phase transitions. In particular, for
np=1 there is no phase transition between the even Haldane phase and the cluster rung-singlet phase while for other odd
np there is a first-order phase transition. Our paper provides comprehensive phase diagrams for these cluster-based models and may be helpful to understand experiments on related materials.