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arXiv:0708.3633 · Physical Review B

Quantum critical scaling behavior of deconfined spinons

Flavio S. Nogueira, Steinar Kragset, Asle Sudbø

Published Dec 6, 2007• 30 citations
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Abstract

We perform a renormalization group analysis of some important effective field theoretic models for deconfined spinons. We show that deconfined spinons are critical for an isotropic $\mathrm{SU}(N)$ Heisenberg antiferromagnet, if $N$ is large enough. We argue that nonperturbatively this result should persist down to $N=2$ and provide further evidence for the so-called deconfined quantum criticality scenario. Deconfined spinons are also shown to be critical for the case describing a transition between quantum spin nematic and dimerized phases. On the other hand, the deconfined quantum criticality scenario is shown to fail for a class of easy-plane models. For the cases where deconfined quantum criticality occurs, we calculate the critical exponent $\ensuremath{\eta}$ for the decay of the two-spin correlation function to first-order in $ϵ=4\ensuremath{-}d$. We also note the scaling relation $\ensuremath{\eta}=d+2(1\ensuremath{-}\ensuremath{\varphi}∕\ensuremath{\nu})$ connecting the exponent $\ensuremath{\eta}$ for the decay to the correlation length exponent $\ensuremath{\nu}$ and the crossover exponent $\ensuremath{\varphi}$.

DOI
10.1103/physrevb.76.220403

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We perform a renormalization group analysis of some important effective field theoretic models for deconfined spinons. We show that deconfined spinons are critical for an isotropic SU(N)\mathrm{SU}(N)SU(N) Heisenberg antiferromagnet, if NNN is large enough. We argue that nonperturbatively this result should persist down to N=2N=2N=2 and provide further evidence for the so-called deconfined quantum criticality scenario. Deconfined spinons are also shown to be critical for the case describing a transition between quantum spin nematic and dimerized phases. On the other hand, the deconfined quantum criticality scenario is shown to fail for a class of easy-plane models. For the cases where deconfined quantum criticality occurs, we calculate the critical exponent \ensuremathη\ensuremath{\eta}\ensuremathη for the decay of the two-spin correlation function to first-order in ϵ=4\ensuremath−dϵ=4\ensuremath{-}dϵ=4\ensuremath−d. We also note the scaling relation \ensuremathη=d+2(1\ensuremath−\ensuremathφ∕\ensuremathν)\ensuremath{\eta}=d+2(1\ensuremath{-}\ensuremath{\varphi}∕\ensuremath{\nu})\ensuremathη=d+2(1\ensuremath−\ensuremathφ∕\ensuremathν) connecting the exponent \ensuremathη\ensuremath{\eta}\ensuremathη for the decay to the correlation length exponent \ensuremathν\ensuremath{\nu}\ensuremathν and the crossover exponent \ensuremathφ\ensuremath{\varphi}\ensuremathφ.
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