Spectrum of conformal gauge theories on a torus

Thomson, Alex; Sachdev, Subir

doi:10.1103/physrevb.95.205128

Cited by 17 publications

(17 citation statements)

References 49 publications

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“…Note Added -After the completion of our work, we learned about an interesting work by A. Thomson and S. Sachdev 43 , which studies disorder effects in QED 3 with a different scope and methodology. We thank them for sharing a draft of their manuscript with us prior to publication.…”

Section: Discussionmentioning

confidence: 99%

Metallic phases from disordered (2+1)-dimensional quantum electrodynamics

Goswami

Goldman

2017

Phys. Rev. B

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Metallic phases have been observed in several disordered two dimensional (2d) systems, including thin films near superconductor-insulator transitions and quantum Hall systems near plateau transitions. The existence of 2d metallic phases at zero temperature generally requires an interplay of disorder and interaction effects. Consequently, experimental observations of 2d metallic behavior have largely defied explanation. We formulate a general stability criterion for strongly interacting, massless Dirac fermions against disorder, which describe metallic ground states with vanishing density of states. We show that (2+1)-dimensional quantum electrodynamics (QED3) with a large, even number of fermion flavors remains metallic in the presence of weak scalar potential disorder due to the dynamic screening of disorder by gauge fluctuations. We also show that QED3 with weak mass disorder exhibits a stable, dirty metallic phase in which both interactions and disorder play important roles.

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Section: Discussionmentioning

confidence: 99%

Metallic phases from disordered (2+1)-dimensional quantum electrodynamics

Goswami

Goldman

2017

Phys. Rev. B

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“…In previous works, analysis of the torus spectrum has been used to study exotic deconfined quantum criticality, including transitions into phases with Z 2 topological order [1, 2] and conformal gauge theories coupled to fermionic matter [3].…”

Section: Introductionmentioning

confidence: 99%

Spectrum of the Wilson-Fisher conformal field theory on the torus

et al. 2017

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We study the finite-size spectrum of the O(N ) symmetric Wilson-Fisher conformal field theory (CFT) on the d = 2 spatial-dimension torus using the expansion in = 3 − d. This is done by deriving a set of universal effective Hamiltonians describing fluctuations of the zero momentum modes. The effective Hamiltonians take the form of N -dimensional quantum anharmonic oscillators, which are shown to be strongly coupled at the critical point for small . The low-energy spectrum is solved numerically for N = 1, 2, 3, 4. Using exact diagonalization (ED), we also numerically study explicit lattice models known to be in the O(2) and O(3) universality class, obtaining estimates of the low-lying critical spectrum. The analytic and numerical results show excellent agreement and the critical low energy torus spectra are qualitatively different among the studied CFTs, identifying them as a useful fingerprint for detecting the universality class of a quantum critical point.

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“…The estimated values are about twice the extrapolated values, perhaps indicating non-negligible nonpertubative corrections to ∆ Q for smaller N . However, the conclusion that monopole operators with Q = 1, 2, 3 are relevant (∆ Q < 3) at O(2) fixed point still remains true.FINITE-SIZE SPECTRUMRecently, the universal features in the finite-size critical spectrum of operators have been of interest[31][32][33]. Here, we provide a computation of critical spectrum of Dirac monopole at the O(2) fixed point of XY model.…”

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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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Spectrum of conformal gauge theories on a torus

Cited by 17 publications

References 49 publications

Metallic phases from disordered (2+1)-dimensional quantum electrodynamics

Metallic phases from disordered (2+1)-dimensional quantum electrodynamics

Spectrum of the Wilson-Fisher conformal field theory on the torus

Monopole scaling dimension using Monte-Carlo simulation

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