The numerical value of a universal quantity associated with the quantum critical regime, namely χuc2/T, for a two-dimensional (2D) dimerized spin-1/2 antiferromagnet is calculated using the quantum Monte Carlo simulations (QMC). Here χu, c, and T are the uniform susceptibility, the spin-wave velocity, and the temperature, respectively. By simulating large lattices at moderately low temperatures, we find χuc2/T∼0.32. Our estimation of χuc2/T deviates from the related analytic prediction but agrees with recent numerical calculations of other 2D dimerized spin-1/2 antiferromagnets.
The transition from dimerized to uniform phases is studied in terms of spectral weights for spin chains using continuous unitary transformations. The spectral weights in the S=1 channel are computed perturbatively around the limit of strong dimerization. We find that the spectral weight is concentrated mainly in the subspaces with a small number of elementary triplets (triplons), even for vanishing dimerization. So, besides spinons, triplons may be used as elementary excitations in spin chains. We conclude that there is no necessity to use fractional excitations in low-dimensional, undoped, or doped quantum antiferromagnets.
We consider quantum spin systems with dimerization, which at strong coupling have singlet ground states. To account for strong correlations, the
S=1 elementary excitations are described as a dilute Bose gas with infinite on-site repulsion. This approach is applied to the two-layer Heisenberg antiferromagnet at
T=0 with general couplings. Our analytic results for the triplet gap, the excitation spectrum, and the location of the quantum critical point are in excellent agreement with numerical results obtained by dimer series expansions.