Confinement transition of Z2 gauge theories coupled to massless fermions: Emergent quantum chromodynamics and SO(5) symmetry

Snir Gazit*, Fakher F. Assaad, Subir Sachdev, Ashvin Vishwanath, Chong Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

60 Scopus citations

Abstract

We study a model of fermions on the square lattice at half-filling coupled to an Ising gauge theory that was recently shown in Monte Carlo simulations to exhibit Z2 topological order and massless Dirac fermion excitations. On tuning parameters, a confining phase with broken symmetry (an antiferromagnet in one choice of Hamiltonian) was also established, and the transition between these phases was found to be continuous, with coincident onset of symmetry breaking and confinement. While the confinement transition in pure gauge theories is well-understood in terms of condensing magnetic flux excitations, the same transition in the presence of gapless fermions is a challenging problem owing to the statistical interactions between fermions and the condensing flux excitations. The conventional scenario then proceeds via a two-step transition, involving a symmetry-breaking transition leading to gapped fermions followed by confinement. In contrast, here, using quantum Monte Carlo simulations, we provide further evidence for a direct, continuous transition and also find numerical evidence for an enlarged SO(5) symmetry rotating between antiferromagnetism and valence bond solid orders proximate to criticality. Guided by our numerical finding, we develop a field theory description of the direct transition involving an emergent nonabelian [SU(2)] gauge theory and a matrix Higgs field. We contrast our results with the conventional Gross–Neveu–Yukawa transition.

Original languageAmerican English
Pages (from-to)E6987-E6995
JournalProceedings of the National Academy of Sciences of the United States of America
Volume115
Issue number30
DOIs
StatePublished - 24 Jul 2018
Externally publishedYes

Bibliographical note

Funding Information:
by Army Research Office Grant W911NF-17-1-0606 and European Research Council Synergy Grant UQUAM. S.G. and A.V. were supported by National Science Foundation (NSF) Grant DMR-1411343. F.F.A. thanks the Deutsche Forschungsgemeinschaft through Sonderforschungsbereiche 1170 ToCoTronics for financial support. This research was supported by NSF Grant DMR-1664842 (to S.S.). Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation. S.S. also acknowledges support from Cenovus Energy at Perimeter Institute. This work was partially performed at the Aspen Center for Physics, which is supported by NSF Grant PHY-1607611, and the Kavli Institute for Theoretical Physics, which is supported by NSF Grant PHY-1125915. A.V. was supported by a Simons Investigator Grant. C.W. was supported by the Harvard Society of Fellows. This research used the Lawrencium computational cluster resource provided by the Information Technology Division at the Lawrence Berkeley National Laboratory, which is supported by Director, Office of Science, Office of Basic Energy Sciences of the US Department of Energy Contract DE-AC02-05CH11231.

Funding Information:
ACKNOWLEDGMENTS. We thank Shubhayu Chatterjee, Tarun Grover, and Mathias Scheurer for valuable discussions: Shubhayu Chatterjee and Mathias Scheurer pointed out that the det H term in Eq. 12 was allowed. S.G. and A.V. thank Mohit Randeria for an earlier collaboration on a related topic. We acknowledge the Gauss Center for Supercomputing (GCS) e.V. (www.gauss-centre.eu/gauss-centre/EN/Home/home node.html) for funding this project by providing computing time on the GCS Supercomputer Super-MUC at Leibniz Supercomputing Center (www.lrz.de). S.G. was supported

Funding Information:
We thank Shubhayu Chatterjee, Tarun Grover, and Mathias Scheurer for valuable discussions: Shubhayu Chatterjee and Mathias Scheurer pointed out that the det H term in Eq. 12 was allowed. S.G. and A.V. thank Mohit Randeria for an earlier collaboration on a related topic. We acknowledge the Gauss Center for Supercomputing (GCS) e.V. (www.gauss-centre.eu/gauss-centre/EN/Home/home node.html) for funding this project by providing computing time on the GCS Supercomputer Super-MUC at Leibniz Supercomputing Center (www.lrz.de). S.G. was supported by Army Research Office Grant W911NF-17-1-0606 and European Research Council Synergy Grant UQUAM. S.G. and A.V. were supported by National Science Foundation (NSF) Grant DMR-1411343. F.F.A. thanks the Deutsche Forschungsgemeinschaft through Sonderforschungsbereiche 1170 ToCoTronics for financial support. This research was supported by NSF Grant DMR-1664842 (to S.S.). Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation. S.S. also acknowledges support from Cenovus Energy at Perimeter Institute. This work was partially performed at the Aspen Center for Physics, which is supported by NSF Grant PHY-1607611, and the Kavli Institute for Theoretical Physics, which is supported by NSF Grant PHY-1125915. A.V. was supported by a Simons Investigator Grant. C.W. was supported by the Harvard Society of Fellows. This research used the Lawrencium computational cluster resource provided by the Information Technology Division at the Lawrence Berkeley National Laboratory, which is supported by Director, Office of Science, Office of Basic Energy Sciences of the US Department of Energy Contract DE-AC02-05CH11231.

Publisher Copyright:
© 2018 National Academy of Sciences. All Rights Reserved.

Keywords

  • Antiferromagnetism
  • Confinement
  • Deconfined criticality
  • Emergent symmetry
  • Fractionalization

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