Neel order in square and triangular lattice Heisenberg models

TL;DR

This paper demonstrates the effective use of DMRG for studying magnetic order in 2D Heisenberg models, introduces improved finite-size scaling methods, and provides precise estimates of order parameters for square and triangular lattices.

Contribution

The paper introduces refined extrapolation techniques and cluster sequences for DMRG, enabling accurate analysis of magnetic order in 2D lattice models.

Findings

Accurate determination of the thermodynamic limit of magnetization in square lattice.

Verification of three-sublattice magnetic order in the triangular lattice.

Estimated order parameter for the triangular lattice M = 0.205(15).

Abstract

Using examples of the square- and triangular-lattice Heisenberg models we demonstrate that the density matrix renormalization group method (DMRG) can be effectively used to study magnetic ordering in two-dimensional lattice spin models. We show that local quantities in DMRG calculations, such as the on-site magnetization M, should be extrapolated with the truncation error, not with its square root, as previously assumed. We also introduce convenient sequences of clusters, using cylindrical boundary conditions and pinning magnetic fields, which provide for rapidly converging finite-size scaling. This scaling behavior on our clusters is clarified using finite-size analysis of the effective sigma-model and finite-size spin-wave theory. The resulting greatly improved extrapolations allow us to determine the thermodynamic limit of M for the square lattice with an error comparable to quantum Monte Carlo. For the triangular lattice, we verify the existence of three-sublattice magnetic order, and estimate the order parameter to be M = 0.205(15).