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

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

2005-09-15

arxiv.org/abs/cond-mat/0509390v2

J. Stat. Mech. (2005) P12001

Physics

Condensed Matter

Strongly Correlated Electrons

27 pages, 12 figures. RG flow added. Final version to appear in JSTAT

Scientific paper

10.1088/1742-5468/2005/12/P12001

Antiferromagnetic Hamiltonians with short-range, non-frustrating interactions are well-known to exhibit long range magnetic order in dimensions, $d\geq 2$ 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 lambda, 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.

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