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 J 1 -J 2 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 Z 2 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 Z 2 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 J 2 /J 1 : Néel, gapless Z 2 spin liquid, and valence bond solid.
Diffusion-driven patterns appear on curved surfaces in many settings, initiated by unstable modes of an underlying Laplacian operator. On a flat surface or perfect sphere, the patterns are degenerate, reflecting translational/rotational symmetry. Deformations, e.g. by a bulge or indentation, break symmetry and can pin a pattern. We adapt methods of conformal mapping and perturbation theory to examine how curvature inhomogeneities select and pin patterns, and confirm the results numerically. The theory provides an analogy to quantum mechanics in a geometry-dependent potential and yields intuitive implications for cell membranes, tissues, thin films, and noise-induced quasipatterns.
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 of N f = 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 with π -flux per plaquette in the ℤ 2 center of SU(2). This theory has an emergent SO(5) f global symmetry and is presumed to confine at low energies to the Néel state. At nonzero doping (or smaller Hubbard repulsion U at half-filling), we argue that confinement occurs via the Higgs condensation of bosonic chargons carrying fundamental SU(2) gauge charges also moving in π ℤ 2 -flux. At half-filling, the low-energy theory of the Higgs sector has N b = 2 relativistic bosons with a possible emergent SO(5) b global symmetry describing rotations between a d -wave superconductor, period-2 charge stripes, and the time-reversal breaking “ d -density wave” state. We propose a conformal SU(2) gauge theory with N f = 2 fundamental fermions, N b = 2 fundamental bosons, and a SO(5) f ×SO(5) b global symmetry, which describes a deconfined quantum critical point between a confining state which breaks SO(5) f and 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 and d -wave superconductivity. A similar theory applies at nonzero doping and large U , with longer-range couplings of the chargons leading to charge order with longer periods.
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