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arXiv · 1807.04958

Deconfined criticality from the QED$_3$-Gross-Neveu model at three loops

Bernhard Ihrig·Lukas Janssen·Luminita N. Mihaila·Michael M. Scherer
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Abstract

The QED$_3$-Gross-Neveu model is a (2+1)-dimensional U(1) gauge theory involving Dirac fermions and a critical real scalar field. This theory has recently been argued to represent a dual description of the deconfined quantum critical point between Neel and valence bond solid orders in frustrated quantum magnets. We study the critical behavior of the QED$_3$-Gross-Neveu model by means of an epsilon expansion around the upper critical space-time dimension of $D_c^+=4$ up to the three-loop order. Estimates for critical exponents in 2+1 dimensions are obtained by evaluating the different Pade approximants of their series expansion in epsilon. We find that these estimates, within the spread of the Pade approximants, satisfy a nontrivial scaling relation which follows from the emergent SO(5) symmetry implied by the duality conjecture. We also construct explicit evidence for the equivalence between the QED$_3$-Gross-Neveu model and a corresponding critical four-fermion gauge theory that was previously studied within the 1/N expansion in space-time dimensions 2<D<4.

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Bernhard Ihrig, Lukas Janssen, Luminita N. Mihaila, Michael M. Scherer. 2018-10-02. Deconfined criticality from the QED$_3$-Gross-Neveu model at three loops. https://doi.org/10.1103/physrevb.98.115163

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