Topological aspects and deconfinement of quantum critical points in 2 + 1 dimension antiferromagnets

We point out that intrinsic critical degrees of freedom exist generally below the upper critical dimension. We study 2 + 1 D antiferromagnets and their quantum criticality to develop this physics.; The Neel ordered ground state, besides Goldstones, has gapped skyrmion and anti-skyrmion topological excitations. We show that in 2 + 1 D antiferromagnets skyrmions have nonzero probability of existence at criticality at arbitrary low energies. Hence skyrmion fluctuations need to be included when calculating quantum critical properties.; We found exact solutions composed of skyrmion and antiskyrmion superpositions, which we call topolons. We include topolons in the partition function and renormalize by integrating out small size topolons and short wavelength Goldstones. We obtain the correlation length exponent nu = 0.9297 and the anomalous dimension eta = 0.3381. Since it is not clear that we have found the physics of deconfined intrinsic quantum critical excitations, we move to study the quantum paramagnetic phase and the approach to criticality from such a phase.; The Neel magnetization of 2 + 1 D antiferromagnets consists of quark-like spin 1/2 constituents, spinons, which are confined in the Neel ordered and quantum paramagnetic phases. The confinement in the paramagnetic phase is understood as arising from instanton events. We find that irrespective of the intrinsic spin of the antiferromagnet, instantons disappear at the critical point because instanton tunneling becomes infinitely costly and has zero probability at criticality. Berry phase terms relevant to the paramagnetic phase vanish at criticality, but make the confinement length scale diverge more strongly for half-integer spins, next strongest for odd integer spins, and weakest for even integer spins. There is an emergent photon at the critical point, but the "semimetallic" nature of critical spinous screens such photon, making it irrelevant to long distance physics. Hence deconfined spinons are strictly free.; The effective field theory at the quantum critical point is derived. It consists of deconfined, massless, spinons with a 1/r&ar; 2-t2 retarded interaction and a static 1/r&ar; interaction, so spinons are essentially free at large separations. A unique prediction is all anomalous exponent eta = 1. Experimentally measurable signatures of deconfined quantum critical spinons are calculated.