Abstract
Recent sign-problem-free quantum Monte Carlo simulations of (2+1)-dimensional lattice quantum electrodynamics (QED3) with N f flavors of fermions on the square lattice have found evidence of continuous quantum phase transitions between a critical phase and a gapped valence-bond-solid (VBS) phase for flavor numbers N f = 4, 6, and 8. We derive the critical theory for these transitions, the chiral O(2) QED3-Gross–Neveu model, and show that the latter is equivalent to the gauged Nambu–Jona-Lasinio model. Using known large-N f results for the latter, we estimate the order parameter anomalous dimension and the correlation length exponent for the transitions mentioned above. We obtain large-N f results for the dimensions of fermion bilinear operators, in both the gauged and ungauged chiral O(2) Gross–Neveu models, which, respectively, describe the long-distance power-law decay of two-particle correlation functions at the VBS transition in lattice QED3 and the Kekulé-VBS transition for correlated fermions on the honeycomb lattice.
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Acknowledgements
We thank the CRM and the QTS-XI committee for organizing this excellent conference. We thank J. A. Gracey, P. Marquard, and N. Zerf for collaboration on related topics, É. Dupuis, S. Giombi, I. F. Herbut, I. R. Klebanov, Z. Y. Meng, A. Penin, M. M. Scherer, and W. Witczak-Krempa for useful discussions, and NSERC, CIFAR, the University of Alberta’s Theoretical Physics Institute (TPI), and the CRC program for financial support.
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Boyack, R., Maciejko, J. (2021). Critical Exponents for the Valence-Bond-Solid Transition in Lattice Quantum Electrodynamics. In: Paranjape, M.B., MacKenzie, R., Thomova, Z., Winternitz, P., Witczak-Krempa, W. (eds) Quantum Theory and Symmetries. CRM Series in Mathematical Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-55777-5_32
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DOI: https://doi.org/10.1007/978-3-030-55777-5_32
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