Dimer–resonating valence bond state of the four-leg Heisenberg ladder: Interference among resonances

Doped and undoped ladders have focused a lot of attention in recent years due to the existence of materials with that structure; some of them are close relatives of the high-Tc oxides as the series Sr2nl22Cu2nlO4nl22 where nl is the number of legs forming the ladder. The undoped Heisenberg spin ladders with nl even are known to be spin liquids with a spin gap and exponential decaying correlation functions. The ground state ~GS! of these low dimensional systems is given by a short-range resonating valence bond ~RVB! ansatz where the topological spin defects are confined. The RVB picture is supported by mean field, density matrix renormalization group ~DMRG!, quantum Monte Carlo ~QMC!, and Lanczos results concerning ladders with nl 52,4 legs and variational Ansätze ~RVA! for the 2-leg ladder. The purpose of this paper is to apply the RVA method to the four-leg spin ladder with the aim of studying in more detail the structure of the short-range RVB state. In the two-leg ladder case the basic mechanism that lowers the GS energy is the resonance between two nearest-neighbor valence bonds. The simplest short-range RVB Ansatz is given by a dimer-RVB state with a single variational parameter u, which gives the amplitude of the resonance. See Ref. 11 for a transfer matrix approach to dimer-RVB states.