Renormalization group method for weakly-coupled quantum chains: application to the spin one-half Heisenberg model

摘要

The Kato-Bloch perturbation formalism is used to present a density-matrixrenormalization-group (DMRG) method for strongly anisotropic two-dimensionalsystems. This method is used to study Heisenberg chains weakly coupled by thetransverse couplings $J_{\perp}$ and $J_{d}$ (along the diagonals). Anextensive comparison of the renormalization group and quantum Monte Carloresults for parameters where the simulations by the latter method are possibleshows a very good agreement between the two methods. It is found, by analyzingground state energies and spin-spin correlation functions, that there is atransition between two ordered magnetic states. When $J_{d}/J_{\perp} \alt0.5$, the ground state displays a N\'eel order. When $J_{d}/J_{\perp} \agt0.5$, a collinear magnetic ground state in which interchain spin correlationsare ferromagnetic becomes stable. In the vicinity of the transition point,$J_{d}/J_{\perp} \approx 0.5$, the ground state is disordered. But, the natureof this disordered ground state is unclear. While the numerical data seem toshow that the chains are disconnected, the possibility of a genuine disorderedtwo-dimensional state, hidden by finite size effects, cannot be excluded.