Scaling dimensions of higher-charge monopoles at deconfined critical points

Sreejith, G. J.; Powell, Stephen

doi:10.1103/physrevb.92.184413

Cited by 43 publications

(34 citation statements)

References 37 publications

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“…Our necessary condition ∆ 1 > 0.580 is consistent with that it is either relevant or irrelevant, depending on the value of ∆ 1 . We note that the scaling dimensions obtained in [25] (i.e. ∆ 1 = 0.579(8), ∆ 2 = 1.42(7) and ∆ 3 = 2.80(3)) are very close to the bound.…”

Section: B Deconfinement Criticality In Néel-vbs Transitionsmentioning

confidence: 60%

“…∆ q > 3 in the table implies that they assume the phase transition is second order even if the lattice symmetry cannot forbid the symmetry breaking operator O q while ∆ q < 3 implies that it is first order. [42,43] no fixed point CDM [25,44] The CP N −1 models with N ≥ 3 have been studied mainly for theoretical interest, but they are regarded as a very good laboratory of the quantum criticality. We summarize the recent estimate of the scaling dimensions taken from the literature in table III and IV.…”

Section: Appendix B: Summary Of Scaling Dimensions In the Literaturementioning

confidence: 99%

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Necessary Condition for Emergent Symmetry from the Conformal Bootstrap

Nakayama

Ohtsuki

2016

Phys. Rev. Lett.

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We use the conformal bootstrap program to derive necessary conditions for emergent symmetry enhancement from discrete symmetry (e.g. Zn) to continuous symmetry (e.g. U (1)) under the renormalization group flow. In three dimensions, in order for Z2 symmetry to be enhanced to U (1) symmetry, the conformal bootstrap program predicts that the scaling dimension of the order parameter field at the infrared conformal fixed point must satisfy ∆1 > 1.08. We also obtain the similar conditions for Z3 symmetry with ∆1 > 0.580 and Z4 symmetry with ∆1 > 0.504 from the simultaneous conformal bootstrap analysis of multiple four-point functions. Our necessary conditions impose severe constraints on many controversial physics such as the chiral phase transition in QCD, the deconfinement criticality in Néel-VBS transitions and anisotropic deformations in critical O(n) models. In some cases, we find that the conformal bootstrap program dashes hopes of emergent symmetry enhancement proposed in the literature.

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Section: B Deconfinement Criticality In Néel-vbs Transitionsmentioning

confidence: 60%

Section: Appendix B: Summary Of Scaling Dimensions In the Literaturementioning

confidence: 99%

Necessary Condition for Emergent Symmetry from the Conformal Bootstrap

Nakayama

Ohtsuki

2016

Phys. Rev. Lett.

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“…For general n there will correspondingly be 6n massless Majorana fermions at the surface. With interactions, we need to consider whether 18 Integrating out the fermion will generate an SO(3) Θ angle at 6π and the Θ angle is 12π once we restrict to SU (2) gauge bundle for some special n the surface is anomaly free. The anomaly on the surface has two parts: 1).…”

Section: Fermionic Deconfined Critical Points In 3 + 1-dmentioning

confidence: 99%

Adventure in Topological Phase Transitions in 3+1 -D: Non-Abelian Deconfined Quantum Criticalities and a Possible Duality

Senthil

2019

Phys. Rev. X

130

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Continuous quantum phase transitions that are beyond the conventional paradigm of fluctuations of a symmetry breaking order parameter are challenging for theory. These phase transitions often involve emergent deconfined gauge fields at the critical points[1-4] as demonstrated in 2 + 1-dimensions. Examples include phase transitions in quantum magnetism as well as those between Symmetry Protected Topological phases. In this paper, we present several examples of Deconfined Quantum Critical Points (DQCP) between Symmetry Protected Topological phases in 3 + 1-D for both bosonic and fermionic systems. Some of the critical theories can be formulated as non-abelian gauge theories either in their Infra-Red free regime, or in the conformal window when they flow to the Banks-Zaks[5, 6] fixed points.We explicitly demonstrate several interesting quantum critical phenomena. We describe situations in which the same phase transition allows for multiple universality classes controlled by distinct fixed points. We exhibit the possibility -which we dub "unnecessary quantum critical points" -of stable generic continuous phase transitions within the same phase. We present examples of interaction driven band-theoryforbidden continuous phase transitions between two distinct band insulators. The understanding we develop leads us to suggest an interesting possible 3 + 1-D field theory duality between SU (2) gauge theory coupled to one massless adjoint Dirac fermion and the theory of a single massless Dirac fermion augmented by a decoupled topological field theory. arXiv:1808.07465v1 [cond-mat.str-el]

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“…For the finite-size scaling study, we used periodic L 3 lattices for L = 12, 16,20,24,28,32 and 36. For each fixed values of L and Q, the different ζ corresponds to independent Monte Carlo simulations.…”

Section: Monopole Critical Exponentsmentioning

confidence: 99%

Monopole scaling dimension using Monte-Carlo simulation

Karthik

2018

Phys. Rev. D

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We present a viable Monte Carlo determination of the scaling dimensions ∆ Q of flux Q Abelian monopoles through finite-size scaling analysis of the free energy to introduce the background field of classical Dirac monopole-antimonopole pair at critical points of three-dimensional lattice theories. We validate the method in free fermion theory, and by verifying the particle-vortex duality between the monopole scaling dimension at the inverse-XY fixed point and the charge scaling dimension at the XY fixed point. At the O(2) Wilson-Fisher fixed point, we determine the critical exponents ∆ 1 = 0.13(2), ∆ 2 = 0.29(1) and ∆ 3 = 0.47(2), which we find to be proportional to the finite-size critical spectrum of monopoles on square torus. arXiv:1808.08970v1 [cond-mat.str-el]

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Scaling dimensions of higher-charge monopoles at deconfined critical points

Cited by 43 publications

References 37 publications

Necessary Condition for Emergent Symmetry from the Conformal Bootstrap

Necessary Condition for Emergent Symmetry from the Conformal Bootstrap

Adventure in Topological Phase Transitions in 3+1 -D: Non-Abelian Deconfined Quantum Criticalities and a Possible Duality

Monopole scaling dimension using Monte-Carlo simulation

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