Critical properties of the valence-bond-solid transition in lattice quantum electrodynamics

Zerf, Nikolai; Boyack, Rufus; Marquard, Peter; Gracey, J.A.; Maciejko, Joseph

doi:10.1103/physrevd.101.094505

Cited by 17 publications

(11 citation statements)

References 61 publications

(113 reference statements)

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“…[28; 31] for earlier studies of this model), while the field theory for the transition to the VBS was outlined in Refs. [91][92][93]. In this work, we used the appellation QED 3 -GN to designate the model with U(2N ) symmetry, following the convention of Refs.…”

Section: Other Phase Transitionsmentioning

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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Section: Other Phase Transitionsmentioning

confidence: 99%

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

DuPuis¹,

Boyack²,

Witczak-Krempa³

2021

Preprint

Self Cite

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“…Furthermore, RGEs of purely scalar theories have even been computed up to six loop orders for O(n) [25][26][27][28][29][30][31][32][33][34], O(n)×O(m) [35][36][37] as well as cubic [38][39][40] symmetries. In four-dimensional Gross-Neveu-Yukawa and abelian Higgs models, the renormalisation group has been investigated up to four loops [41][42][43][44][45].…”

Section: Introductionmentioning

confidence: 99%

General scalar renormalisation group equations at three-loop order

Steudtner

2020

J. High Energ. Phys.

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For arbitrary scalar QFTs in four dimensions, renormalisation group equations of quartic and cubic interactions, mass terms, as well as field anomalous dimensions are computed at three-loop order in the $$ \overline{\mathrm{MS}} $$ MS ¯ scheme. Utilising pre-existing literature expressions for a specific model, loop integrals are avoided and templates for general theories are obtained. We reiterate known four-loop expressions, and from those derive β functions for scalar masses and cubic interactions. As an example, the results are applied to compute all renormalisation group equations in U(n) × U(n) scalar theories.

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“…( 1) includes an one-component real scalar field, Σ 1 is a trivial identity matrix in this case, so we have [γ µ , Σ 1 ] = 0 for chiral Ising-GNY model. In the chiral XY universality class for N = 2, the GNY model includes a complex order parameter, now the Yukawa term can be generally written as L ψφ = g ψi (φ 1 + iγ 5 φ 2 )ψ i , where {γ 5 , γ µ } = 0 and the explicit choice of γ 5 depends on the specific model [20,87,88]. Note that γ 5 S ψ (p) = −S ψ (p)γ 5 , where S ψ (p) is the fermion propagator.…”

Section: The Gross-neveu-yukawa Modelmentioning

confidence: 99%

Critical structure and emergent symmetry of Dirac fermion systems

Zhou

2022

Preprint

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Emergent symmetry in Dirac system means that the system acquires an enlargement of two basic symmetries at some special critical point. The continuous quantum criticality between the two symmetry broken phases can be described within the framework of Gross-Neveu-Yukawa (GNY) model. Using the first-order expansion in 4 − dimensions, we study the critical structure and emergent symmetry of the chiral GNY model with N f flavors of four-component Dirac fermions coupled strongly to an O(N ) scalar field under a small O(N )-symmetry breaking perturbation. After determining the stable fixed point, we calculate the inverse correlation length exponent and the anomalous dimensions (bosonic and fermionic) for general N and N f . Further, we discuss the emergent-symmetry and the emergent supersymmetric critical point for N ≥ 4 on the basis of O(N )-GNY model. It turns out that the chiral emergent-O(N ) universality class is physically meaningful if and only if N < 2N f + 4. On this premise, the small O(N )-symmetry breaking perturbation is always irrelevant in the chiral emergent-O(N ) universality class. Our studies show that the emergent symmetry in Dirac systems has an upper boundary O(2N f + 3), depending on the flavor numbers N f . As a result, the emergent-O(4) and O(5) symmetries are possible to be found in the systems with fermion flavor N f = 1, and the emergent-O(4), O(5), O(6) and O(7) symmetries are expected to be found in the systems with fermion flavor N f = 2. Our result also suggests some rich transitions with emergent-Z2 × O(2) × O(3) symmetry and so on. Interestingly, in the emergent-O(4) universality class, there is a supersymmetric critical point which is expected to be found in the systems with fermion flavor N f = 1.

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Critical properties of the valence-bond-solid transition in lattice quantum electrodynamics

Cited by 17 publications

References 61 publications

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

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

General scalar renormalisation group equations at three-loop order

Critical structure and emergent symmetry of Dirac fermion systems

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