Monopole hierarchy in transitions out of a Dirac spin liquid

Dupuis, Éric; Witczak-Krempa, William

doi:10.1016/j.aop.2021.168496

Cited by 15 publications

(11 citation statements)

References 44 publications

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“…Note that for these monopole operators, as well as for the ones mentioned in the next two subsections and in [56][57][58], the large q expansion works quite well all the way down to q = 1 (this was first observed in the context of the expansion of their dimensions in [59]).…”

Section: The Quartic O(n ) Model In D Dimensions At Large Nmentioning

confidence: 53%

On Convexity of Charged Operators in CFTs and the Weak Gravity Conjecture

Aharony,

Palti

2021

Preprint

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The Weak Gravity Conjecture is typically stated as a bound on the mass-to-charge ratio of a particle in the theory. Alternatively, it has been proposed that its natural formulation is in terms of the existence of a particle which is self-repulsive under all long-range forces. We propose a closely related, but distinct, formulation, which is that it should correspond to a particle with non-negative self-binding energy. This formulation is particularly interesting in anti-de Sitter space, because it has a simple conformal field theory (CFT) dual formulation: let ∆(q) be the dimension of the lowest-dimension operator with charge q under some global U (1) symmetry, then ∆(q) must be a convex function of q. This formulation avoids any reference to holographic dual forces or even to locality in spacetime, and so we make a wild leap, and conjecture that such convexity of the spectrum of charges holds for any (unitary) conformal field theory, not just those that have weakly coupled and weakly curved duals. This Charge Convexity Conjecture, and its natural generalization to larger global symmetry groups, can be tested in various examples where anomalous dimensions can be computed, by perturbation theory, 1/N expansions and semi-classical methods. In all examples that we tested we find that the conjecture holds. We do not yet understand from the CFT point of view why this is true.

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Section: The Quartic O(n ) Model In D Dimensions At Large Nmentioning

confidence: 53%

On Convexity of Charged Operators in CFTs and the Weak Gravity Conjecture

Aharony,

Palti

2021

Preprint

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“…It would be interesting to study monopole operators in the other gauged GN models that we briefly discussed, notably the model describing the transition to an AFM [31][32][33]. Another interesting aspect to consider that was not included in this work is the case of monopole operators in the pure-GN model.…”

Section: Discussionmentioning

confidence: 99%

Anomalous dimensions of monopole operators at the transitions between Dirac and topological spin liquids

DuPuis¹,

Boyack²,

Witczak-Krempa³

2021

Preprint

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Monopole operators are studied at certain quantum critical points between a Dirac spin liquid and topological quantum spin liquids (QSLs): chiral and Z2 QSLs. These quantum phase transitions are described by conformal field theories (CFTs): quantum electrodynamics in 2+1 dimensions with 2N flavors of two-component massless Dirac fermions and a four-fermion interaction term. For the transition to a chiral spin liquid, it is the Gross-Neveu interaction (QED3-GN), while for the transition to the Z2 QSL it is a superconducting pairing term (QED3-Z2GN). Using the state-operator correspondence, we obtain monopole scaling dimensions to sub-leading order in 1/N . For monopoles with a minimal topological charge q = 1/2, the scaling dimension is 2N × 0.26510 at leading-order, with the quantum correction being 0.118911(7) for the chiral spin liquid, and 0.102846(9) for the Z2 case. Although these two anomalous dimensions are nearly equal, the underlying quantum fluctuations possess distinct origins. The analogous result in QED3 is also obtained and we find a sub-leading contribution of −0.038138(5), which is slightly different from the value −0.0383 first obtained in the literature. The scaling dimension of a QED3-GN monopole with minimal charge is very close to the scaling dimensions of other operators predicted to be equal by a conjectured duality between QED3-GN with 2N = 2 flavors and the CP 1 model. Additionally, non-minimally charged monopoles with equal charges on both sides of the duality have similar scaling dimensions. By studying the large-q asymptotics of the scaling dimensions in QED3, QED3-GN, and QED3-Z2GN we verify that the constant O(q 0 ) coefficient precisely matches the universal prediction for CFTs with a global U(1) symmetry. CONTENTS A. Large N non-compact quantum phase transition B. Scalar-gauge kernel C. Gauge invariance Verifications D. Green's function 1. Eigenvalues of determinant operator 2. Green's function E. Eigenkernels 1. First basis 2. Second basis 3. Kernel coefficients for general q F. Results for the q = 1/2 computations G. Remainder coefficients H. Only zero modes contribution in the kernels Generalization I. Fitting procedure for anomalous dimensions J. Monopole scaling dimensions for 1/2 ≤ q ≤ 13 References

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“…Such a modification, if calculated perturbatively in Φ, arises at O(Φ 2 ) -this is still an appreciable shift given the relatively large anisotropy Φ c ≈ 0.46. Previous works have studied the effects of a spin Hall mass on the monopole scaling dimension [44,45], although this perturbation is more tractable as the spin Hall mass is diagonal in the basis of spinor monopole harmonics. In Appendix F, we outline the structure of a perturbative calculation for calculating the O(Φ 2 ) corrections to the monopole scaling dimension.…”

Section: Monopolesmentioning

confidence: 99%

“…Additionally, we briefly comment on the relation between this velocity anisotropy and the monopole quantum numbers. Prior studies on the effects of a spin Hall mass [44,45] have found that the presence of such a term induces a spin polarization on the monopoles. Each fermion flavor has a zero mode in the presence of a monopole, and half of these zero modes must be filled in order to maintain gauge neutrality of the monopole.…”

Section: Monopolesmentioning

confidence: 99%

Anisotropic deconfined criticality in Dirac spin liquids

Shackleton,

Sachdev

2022

Preprint

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We analyze a Higgs transition from a U(1) Dirac spin liquid to a gapless Z 2 spin liquid. This Z 2 spin liquid is of relevance to the spin S = 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 (the J 1 -J 2 model), 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 Z 2 spin liquid of the J 1 -J 2 model 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 Z 2 spin liquid in a 1/N f expansion, with N f proportional to the number of fermions, we find a stable fixed point with an anisotropic spinon dispersion and a dynamical critical exponent z = 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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Monopole hierarchy in transitions out of a Dirac spin liquid

Cited by 15 publications

References 44 publications

On Convexity of Charged Operators in CFTs and the Weak Gravity Conjecture

On Convexity of Charged Operators in CFTs and the Weak Gravity Conjecture

Anomalous dimensions of monopole operators at the transitions between Dirac and topological spin liquids

Anisotropic deconfined criticality in Dirac spin liquids

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