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A<sc>bstract</sc> We analyze a Higgs transition from a U(1) Dirac spin liquid to a gapless ℤ2spin liquid. This ℤ2spin liquid is of relevance to the spinS= 1/2 square lattice antiferromagnet, where recent numerical studies have given evidence for such a phase existing in the regime of high frustration between nearest neighbor and next-nearest neighbor antiferromagnetic interactions (theJ1-J2model), appearing in a parameter regime between the vanishing of Néel order and the onset of valence bond solid ordering. The proximate Dirac spin liquid is unstable to monopole proliferation on the square lattice, ultimately leading to Néel or valence bond solid ordering. As such, we conjecture that this Higgs transition describes the critical theory separating the gapless ℤ2spin liquid of theJ1-J2model from one of the two proximate ordered phases. The transition into the other ordered phase can be described in a unified manner via a transition into an unstable SU(2) spin liquid, which we have analyzed in prior work. By studying the deconfined critical theory separating the U(1) Dirac spin liquid from the gapless ℤ2spin liquid in a 1/Nfexpansion, withNfproportional to the number of fermions, we find a stable fixed point with an anisotropic spinon dispersion and a dynamical critical exponentz≠ 1. We analyze the consequences of this anisotropic dispersion by calculating the angular profiles of the equal-time Néel and valence bond solid correlation functions, and we find them to be distinct. We also note the influence of the anisotropy on the scaling dimension of monopoles.
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A model of d -wave superconductivity, antiferromagnetism, and charge order on the square lattice
We describe the confining instabilities of a proposed quantum spin liquid underlying the pseudogap metal state of the hole-doped cuprates. The spin liquid can be described by a SU(2) gauge theory ofNf= 2 massless Dirac fermions carrying fundamental gauge charges—this is the low-energy theory of a mean-field state of fermionic spinons moving on the square lattice withπ-flux per plaquette in the ℤ2center of SU(2). This theory has an emergent SO(5)fglobal symmetry and is presumed to confine at low energies to the Néel state. At nonzero doping (or smaller Hubbard repulsionUat half-filling), we argue that confinement occurs via the Higgs condensation of bosonic chargons carrying fundamental SU(2) gauge charges also moving inπℤ2-flux. At half-filling, the low-energy theory of the Higgs sector hasNb= 2 relativistic bosons with a possible emergent SO(5)bglobal symmetry describing rotations between ad-wave superconductor, period-2 charge stripes, and the time-reversal breaking “d-density wave” state. We propose a conformal SU(2) gauge theory withNf= 2 fundamental fermions,Nb= 2 fundamental bosons, and a SO(5)f×SO(5)bglobal symmetry, which describes a deconfined quantum critical point between a confining state which breaks SO(5)fand a confining state which breaks SO(5)b. The pattern of symmetry breaking within both SO(5)s is determined by terms likely irrelevant at the critical point, which can be chosen to obtain a transition between Néel order andd-wave superconductivity. A similar theory applies at nonzero doping and largeU, with longer-range couplings of the chargons leading to charge order with longer periods.
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- Award ID(s):
- 2002850
- PAR ID:
- 10592240
- Publisher / Repository:
- Proceedings of the National Academy of Sciences
- Date Published:
- Journal Name:
- Proceedings of the National Academy of Sciences
- Volume:
- 120
- Issue:
- 21
- ISSN:
- 0027-8424
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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