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Fermionic Minimal Models.

Chang-Tse Hsieh1,2, Yu Nakayama3, Yuji Tachikawa1

  • 1Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo, Kashiwa, Chiba 277-8583, Japan.

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Researchers have identified fermionic minimal models in 1+1D conformal field theory for various central charges. These models, featuring half-integral spin operators, generalize known fermionic theories and are realized via explicit Hamiltonians.

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Area of Science:

  • Theoretical physics
  • Quantum field theory
  • Condensed matter physics

Background:

  • Conformal field theories (CFTs) are crucial in understanding critical phenomena.
  • Minimal models are a specific class of CFTs with finite numbers of primary fields.
  • Fermionic systems exhibit unique properties related to half-integral spin operators.

Purpose of the Study:

  • To establish the existence of fermionic minimal models for a continuous range of central charges.
  • To generalize known fermionic theories like the Majorana fermion and N=1 supersymmetric minimal model.
  • To provide concrete realizations of these models using Hamiltonians.

Main Methods:

  • Construction of 1+1 dimensional conformal field theories.
  • Analysis of operator spectra for half-integral spins.
  • Development of explicit Hamiltonians for Majorana chains.

Main Results:

  • Demonstrated the existence of a fermionic minimal model for each central charge c=1-6/m(m+1), with m≥3.
  • Showcased that these models contain operators with half-integral spins.
  • Provided explicit Hamiltonians on Majorana chains that realize these models.

Conclusions:

  • The study establishes a broad class of fermionic minimal models within 1+1D CFT.
  • These findings extend our understanding of minimal models and their fermionic realizations.
  • The explicit Hamiltonians offer a pathway for experimental or numerical investigations.