Renormalization-group method for weakly coupled quantum chains: Application to the spin-1/2 Heisenberg model

The Kato-Bloch perturbation formalism is used to present a density-matrix renormalization-group method for strongly anisotropic two-dimensional systems. This method is used to study Heisenberg chains weakly coupled by the transverse couplings J_⊥ and J_d (along the diagonals). An extensive comparison of the renormalization group and quantum Monte Carlo results for parameters where the simulations by the latter method are possible shows a very good agreement between the two methods. It is found, by analyzing ground state energies and spin-spin correlation functions, that there is a transition between two ordered magnetic states. When J_d/J _⊥≲0.5, the ground state displays a Néel order. When J_d/J_⊥≳0.5, a collinear magnetic ground state in which interchain spin correlations are ferromagnetic becomes stable. In the vicinity of the transition point, J_d/J_⊥≈0.5, the ground state is disordered. But, the nature of this disordered ground state is unclear. While the numerical data seem to show that the chains are disconnected, the possibility of a genuine disordered two-dimensional state, hidden by finite size effects, cannot be excluded.