Using helical boundary conditions, we present exact-diagonalization results for two-dimensional spin-1/2 antiferromagnetic Heisenberg systems. Energy and staggered magnetization for an infinite system are obtained by extrapolation from finite square systems. Comparisons with the results obtained for periodic boundary conditions are made.
Abstract Motivated by the need for high-precision benchmark results for basic quantum many-body models, 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 → 0 limit, with significantly reduced statistical errors relative to previous works. Results for periodic L × L lattices with L ∈ [ 6 , 96 ] are tabulated versus L and extrapolations to infinite system size are carried out. The relative statistical errors of finite-size energies are below 10 −7 . The extrapolated ground state energy density is e 0 = − 0.669 441 857 ( 7 ) , where the number within parentheses is the statistical error (one standard deviation) of the preceding digit. This value represents an improvement in precision of three orders of magnitude over the previous 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 = 0.307 447 ( 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 s 2 agrees with the value from chiral perturbation theory and the presence of a factor ln γ ( L ) in the second-order correction is also confirmed, with the previously unknown value of the exponent being γ = 0.82 ( 4 ) . The finite-size corrections to the staggered susceptibility point to logarithmic corrections in this quantity as well. 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.
The ground-state energy, staggered magnetization, and correlation function are computed for the two-dimensional spin-(1/2 quantum antiferromagnetic Heisenberg model (believed to be relevant to the high-temperature superconducting materials without doping) on lattices up to 24\ifmmode\times\else\texttimes\fi{}24 by Monte Carlo methods extrapolated to zero temperature. A more accurate value for the ground-state energy is determined by the method of Neumann and Ulam by extrapolating from lattices up to 12\ifmmode\times\else\texttimes\fi{}12.
The present work investigates the influence of external perturbations on the ground
states of spin-1/2 antiferromagnetic Heisenberg chains and two-dimensional spin
lattices. The lifting of the well-known zero-energy excitations (soft modes) of
the unperturbed Heisenberg chain due to suitably chosen periodicities of applied
perturbations is presented. The evolution of excitation energies and transition
matrix elements is described by a complete set of differential equations and scaling
solutions for small perturbations are discussed. A variety of topic
quasi-one-dimensional spin systems (spin-Peierls chain, spin ladders in different
geometries) are then embedded in the descriptive scheme of periodically perturbed
Heisenberg chains. In particular, the energy gaps and, most noticeable, the formation
of magnetization plateaus occurring in these systems are discussed in a single
prediction scheme related to the soft mode positions of the previously unperturbed
chain. Plateaus due to various kinds of perturbations are furthermore shown to be
observable in static correlation functions of the perturbed chain. Particular emphasis
is laid on the consideration of processes of spontaneous breaking of symmetry.
The latter aspect is discussed for translationally invariant perturbations that
do not provide an explicit change of the periodicity of the spin system. The
presented investigations finally turn to two-dimensional spin systems first addressing
the formation of a non-zero staggered magnetization (long range order) for increased
two-dimensionality in terms of a translationally invariant perturbed (helical) spin
system. Finally, first stages of a present study on the formation of magnetization
plateaus in square spin lattices with frustrating diagonal couplings are given.
We present numerical exact results for the ground state and the low-lying excitations for the spin-1/2 J1-J2 Heisenberg antiferromagnet on finite square lattices of up to N = 40 sites. Using finite-size extrapolation we determine the ground-state energy, the magnetic order parameters, the spin gap, the uniform susceptibility, as well as the spin-wave velocity and the spin stiffness as functions of the frustration parameter J2/J1. In agreement with the generally excepted scenario we find semiclassical magnetically ordered phases for J2 < J c1 2 and J2> J c2 2 separated by a gapful quantum paramagnetic phase. We estimate Jc1 2 ≈ 0.35J1 and J c2 2 ≈ 0.66J1. PACS codes: 75.10.Jm Quantized spin models 75.45.+j Macroscopic quantum phenomena in magnetic systems 1