High-precision ground state parameters of the two-dimensional spin-1/2 Heisenberg model on the square lattice

TL;DR

This paper provides highly precise ground state parameters of the 2D spin-1/2 Heisenberg model on a square lattice, using extensive quantum Monte Carlo simulations and extrapolations to the thermodynamic limit.

Contribution

It offers the most accurate estimates of ground state energy, magnetization, and susceptibilities, confirming theoretical predictions and improving previous results by orders of magnitude.

Findings

Ground state energy density e_0 = -0.669441857(7) with three orders of magnitude improvement.

Sublattice magnetization m_s = 0.307447(2) with reduced statistical error.

Finite-size corrections match chiral perturbation theory predictions, including logarithmic factors.

Abstract

Several ground state properties of the square-lattice $S=1/2$ Heisenberg antiferromagnet are computed (the energy, order parameter, spin stiffness, spinwave velocity, long-wavelength susceptibility, and staggered susceptibility) using extensive quantum Monte Carlo simulations with the stochastic series expansion method. Moderately sized lattices are studied at temperatures $T$ sufficiently low to realize the $T \to 0$ limit. Results for periodic $L\times L$ lattices with $L \in [6,96]$ are tabulated versus $L$ and extrapolations to infinite system size are carried out. The extrapolated ground state energy density is $e_0=-0.669441857(7)$, which represents an improvement in precision of three orders of magnitude over the previously best result. The leading and subleading finite-size corrections to $e_0$ are in full quantitative agreement with predictions from chiral perturbation theory, thus further supporting the soundness of both the extrapolations and the theory. The extrapolated sublattice magnetization is $m_s=0.307447(2)$, which agrees well with previous estimates but with a much smaller statistical error. The coefficient of the linear in $L^{-1}$ correction to $m^2_s$ agrees with the value from chiral perturbation theory and the presence of a factor $\ln^\gamma(L)$ in the second-order correction is also confirmed, with the previously not known value of the exponent being $\gamma = 0.82(4)$. The finite-size corrections to the staggered susceptibility point to logarithmic corrections also in this quantity. To facilitate benchmarking of methods for which periodic boundary conditions are challenging, results for systems with open and cylindrical boundaries are also listed and their spatially inhomogeneous order parameters are analyzed.