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

TL;DR

This paper develops a renormalization group method based on the density-matrix approach to study weakly coupled quantum spin chains, revealing a magnetic phase transition and analyzing ground state properties.

Contribution

It introduces a novel RG method for anisotropic 2D quantum systems and compares its results with quantum Monte Carlo, confirming phase transition behavior.

Findings

Identifies a transition from Néel to collinear magnetic order at J_d/J_⊥ ≈ 0.5.

Shows good agreement between RG and quantum Monte Carlo results.

Suggests the presence of a disordered ground state near the transition point.

Abstract

The Kato-Bloch perturbation formalism is used to present a density-matrix renormalization-group (DMRG) method for strongly anisotropic two-dimensional systems. This method is used to study Heisenberg chains weakly coupled by the transverse couplings $J_{\perp}$ 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 $J_{d}/J_{\perp} \alt 0.5$, the ground state displays a N\'eel order. When $J_{d}/J_{\perp} \agt 0.5$, a collinear magnetic ground state in which interchain spin correlations are ferromagnetic becomes stable. In the vicinity of the transition point, $J_{d}/J_{\perp} \approx 0.5$, 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.