Critical phenomena and quantum phase transition in long range Heisenberg antiferromagnetic chains

Antiferromagnetic Hamiltonians with short range, non-frustrating interactions are well known to exhibit long range magnetic order in dimensions d >= 2 but exhibit only quasi-long-range order, with power-law decay of correlations, in d = 1 (for half-integer spin). On the other hand, non-frustrating long range interactions can induce long range order in d = 1. We study Hamiltonians in which the long range interactions have an adjustable amplitude., as well as an adjustable power law 1/|x|(alpha), using a combination of quantum Monte Carlo and analytic methods: spin-wave, large N non-linear sigma model, and renormalization group methods. We map out the phase diagram in the lambda-alpha plane and study the nature of the critical line separating the phases with long range and quasi-long-range order. We find that this corresponds to a novel line of critical points with continuously varying critical exponents and a dynamical exponent, z < 1.