Strong Coupling Expansions for Antiferromagnetic Heisenberg S=1/2 Ladders

The properties of antiferromagnetic Heisenberg $S=\frac{1}{2}$ ladders with 2, 3, and 4 chains are expanded in the ratio of the intra- and interchain coupling constants. A simple mapping procedure is introduced to relate the 4 and 2-chain ladders which holds down to moderate values of the expansion parameters. A second order calculation of the spin gap to the lowest triplet excitation in the 2- and 4-chain ladders is found to be quite accurate even at the isotropic point where the couplings are equal. Similar expansions and mapping procedures are presented for the 3-chain ladders which are in the same universality class as single chains.Comment: 10 physical pages, uuencoded compressed PostScript file including 12 figures, ETH-TH/942

Bound states of magnons in the S=1/2 quantum spin ladder

We study the excitation spectrum of the two-leg antiferromagnetic S=1/2 Heisenberg ladder. Our approach is based on the description of the excitations as triplets above a strong-coupling singlet ground state. The quasiparticle spectrum is calculated by treating the excitations as a dilute Bose gas with infinite on-site repulsion. We find singlet (S=0) and triplet (S=1) two-particle bound states of the elementary triplets. We argue that bound states generally exist in any dimerized quantum spin model.Comment: 4 REVTeX pages, 4 Postscript figure

Perturbation Theory for Spin Ladders Using Angular-Momentum Coupled Bases

We compute bulk properties of Heisenberg spin-1/2 ladders using Rayleigh-Schr\"odinger perturbation theory in the rung and plaquette bases. We formulate a method to extract high-order perturbative coefficients in the bulk limit from solutions for relatively small finite clusters. For example, a perturbative calculation for an isotropic $2\times 12$ ladder yields an eleventh-order estimate of the ground-state energy per site that is within 0.02% of the density-matrix-renormalization-group (DMRG) value. Moreover, the method also enables a reliable estimate of the radius of convergence of the perturbative expansion. We find that for the rung basis the radius of convergence is $\lambda_c\simeq 0.8$, with $\lambda$ defining the ratio between the coupling along the chain relative to the coupling across the chain. In contrast, for the plaquette basis we estimate a radius of convergence of $\lambda_c\simeq 1.25$. Thus, we conclude that the plaquette basis offers the only currently available perturbative approach which can provide a reliable treatment of the physically interesting case of isotropic $(\lambda=1)$ spin ladders. We illustrate our methods by computing perturbative coefficients for the ground-state energy per site, the gap, and the one-magnon dispersion relation.Comment: 22 pages. 9 figure

Dualities in Spin Ladders

We introduce a set of discrete modular transformations $T_\ell,U_\ell$ and $S_\ell$ in order to study the relationships between the different phases of the Heisenberg ladders obtained with all possible exchange coupling constants. For the 2 legged ladder we show that the $RVB$ phase is invariant under the $S_\ell$ transformation, while the Haldane phase is invariant under $U_\ell$. These two phases are related by $T_\ell$. Moreover there is a "mixed" phase, that is invariant under $T_\ell$, and which under $U_\ell$ becomes the RVB phase, while under $S_\ell$ becomes the Haldane phase. For odd ladders there exists only the $T_\ell$ transformation which, for strong coupling, maps the effective antiferromagnetic spin 1/2 chain into the spin 3/2 chain.Comment: REVTEX file, 5 pages, 2 EPS figure

Optical absorption of spin ladders

We present a theory of phonon-assisted optical two-magnon absorption in two-leg spin-ladders. Based on the strong intra-rung-coupling limit we show that collective excitations of total spin S=0, 1 and 2 exist outside of the two-magnon continuum. It is demonstrated that the singlet collective state has a clear signature in the optical spectrum.Comment: 4 pages, 3 figure

Quantum Monte Carlo Simulation of the Trellis Lattice Heisenberg Model for SrCu2_2O3_3 and CaV2_2O5_5

We study the spin-1/2 trellis lattice Heisenberg model, a coupled spin ladder system, both by perturbation around the dimer limit and by quantum Monte Carlo simulations. We discuss the influence of the inter-ladder coupling on the spin gap and the dispersion, and present results for the temperature dependence of the uniform susceptibility. The latter was found to be parameterized well by a mean-field type scaling ansatz. Finally we discuss fits of experimental measurements on SrCu$_2$O$_3$ and CaV$_2$O$_5$ to our results.Comment: 7 pages, 8 figure

On the ground state energy scaling in quasi-rung-dimerized spin ladders

On the basis of periodic boundary conditions we study perturbatively a large N asymptotics (N is the number of rungs) for the ground state energy density and gas parameter of a spin ladder with slightly destroyed rung-dimerization. Exactly rung-dimerized spin ladder is treated as the reference model. Explicit perturbative formulas are obtained for three special classes of spin ladders.Comment: 4 page

Exact results for the thermal and magnetic properties of strong coupling ladder compounds

We investigate the thermal and magnetic properties of the integrable su(4) ladder model by means of the quantum transfer matrix method. The magnetic susceptibility, specific heat, magnetic entropy and high field magnetization are evaluated from the free energy derived via the recently proposed method of high temperature expansion for exactly solved models. We show that the integrable model can be used to describe the physics of the strong coupling ladder compounds. Excellent agreement is seen between the theoretical results and the experimental data for the known ladder compounds (5IAP)$_2$CuBr$_4$$\cdot$2H$_2$O, Cu$_{2}$(C$_5$H$_{12}$N$_2$)$_2$Cl$_4$ etc.Comment: 10 pages, 5 figure

Electronic and Magnetic Structure of LaCuO2.5_{2.5}

The recently-discovered ``ladder'' compound LaCuO$_{2.5}$ has been found to admit hole doping without altering its structure of coupled copper oxide ladders. While susceptibility measurements on the parent compound suggest a spin gap and a spin-liquid state, NMR results indicate magnetic order at low temperatures. These seemingly contradictory results may be reconciled if in fact the magnetic state is near the crossover from spin liquid to antiferromagnet, and we investigate this possibility. From a tight-binding fit to the valence LDA bandstructure, we deduce that the strength of the interladder hopping term is approximately half that of intraladder hopping, showing that the material is three-dimensional in character. A mean-field treatment of the insulating magnetic state gives a spin-liquid phase whose spin gap decreases with increasing interladder coupling, vanishing (signalling a transition to the ordered phase) at a value somewhat below that obtained for LaCuO$_{2.5}$. The introduction of an on-site repulsion term, $U$, to the band scheme causes a transition to an antiferromagnetic insulator for rather small but finite values of $U$, reflecting the predominance of (one-dimensional) ladder behavior, and an absence of any special nesting features.Comment: 8 pages + 5 figure