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Deconfined criticality and a gapless Z₂ spin liquid in the square-lattice antiferromagnet

Shackleton, Henry and Thomson, Alex and Sachdev, Subir (2021) Deconfined criticality and a gapless Z₂ spin liquid in the square-lattice antiferromagnet. Physical Review B, 104 (4). Art. No. 045110. ISSN 2469-9950. doi:10.1103/physrevb.104.045110.

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The theory for the vanishing of Néel order in the spin S = 1/2 square lattice antiferromagnet has been the focus of attention for many decades. A consensus appears to have emerged in recent numerical studies on the antiferromagnet with first and second neighbor exchange interactions (the J₁−J₂ model): A gapless spin liquid is present for a narrow window of parameters between the vanishing of the Néel order and the onset of a gapped valence bond solid state. We propose a deconfined critical SU(2) gauge theory for a transition into a stable Z₂ spin liquid with massless Dirac spinon excitations; on the other side of the critical point, the SU(2) spin liquid (the ‘π-flux’ phase) is presumed to be unstable to confinement to the Néel phase. We identify a dangerously irrelevant coupling in the critical SU(2) gauge theory, which contributes a logarithm-squared renormalization. This critical theory is also not Lorentz invariant and weakly breaks the SO(5) symmetry which rotates between the Néel and valence bond solid order parameters. We also propose a distinct deconfined critical U(1) gauge theory for a transition into the same gapless Z₂ spin liquid; on the other side of the critical point, the U(1) spin liquid (the ‘staggered flux’ phase) is presumed to be unstable to confinement to the valence bond solid. This critical theory has no dangerously irrelevant coupling, dynamic critical exponent z ≠ 1, and no SO(5) symmetry. All of these phases and critical points are unified in a SU(2) gauge theory with Higgs fields and fermionic spinons which can naturally realize the observed sequence of phases with increasing J₂/J₁: Néel, gapless Z₂ spin liquid, and valence bond solid.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Shackleton, Henry0000-0002-1971-6426
Thomson, Alex0000-0002-9938-5048
Sachdev, Subir0000-0002-2432-7070
Additional Information:© 2021 American Physical Society. (Received 29 April 2021; revised 23 June 2021; accepted 23 June 2021; published 6 July 2021) We thank Federico Becca and Anders Sandvik for enlightening discussions which stimulated this work. We are also grateful to Masatoshi Imada, Steve Kivelson, Patrick Ledwith, Ying Ran, T. Senthil, Ashvin Vishwanath, Chong Wang, and Cenke Xu for valuable discussions. This research was supported by the National Science Foundation under Grant No. DMR-2002850. This work was also supported by the Simons Collaboration on Ultra-Quantum Matter, which is a grant from the Simons Foundation (651440, S.S.).
Group:Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Simons Foundation651440
Issue or Number:4
Record Number:CaltechAUTHORS:20210709-212640442
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:109762
Deposited By: George Porter
Deposited On:09 Jul 2021 22:18
Last Modified:16 Nov 2021 19:37

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