Quantitative description of long-range order in the anisotropic spin-1/2 Heisenberg antiferromagnet on the square lattice

Abstract

The quantitative description of long-range order remains a challenge in quantum many-body physics. We provide zero-temperature results from two complementary methods for the ground-state energy per site, the sublattice magnetization, the spin gap, and the transverse spin correlation length for the spin-1/2 anisotropic quantum Heisenberg antiferromagnet on the square lattice. On the one hand, we use exact, large-scale quantum Monte Carlo (QMC) simulations. On the other hand, we use the semi-analytic approach based on continuous similarity transformations in terms of elementary magnon excitations. Our findings confirm the applicability and quantitative validity of both approaches along the full parameter axis from the Ising point to the symmetry-restoring phase transition at the Heisenberg point and further provide quantitative reference results in the thermodynamic limit. In addition, we analytically derive the relation between the dispersion and the correlation length at zero temperature in arbitrary dimension, and discuss improved second-moment QMC estimators.

12 pages, 5 figures

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• Quantum melting of long-range ordered quantum antiferromagnets investigated by momentum-space continuous similarity transformations
• Switching magnetization of quantum antiferromagnets: Schwinger boson mean-field theory compared to exact diagonalization
• Quantum decay of magnons in the unfrustrated honeycomb Heisenberg model
• Anomalous enhancement of Neel order in the $S=1/2$ square lattice Heisenberg model under fictitious magnetic field
• Quantum effects in the magnon spectrum of 2D altermagnets via continuous similarity transformations