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<p>We consider the two-dimensional <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\mathbbm {Z}_{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">Z</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation> lattice gauge theory coupled to fermionic matter. In absence of electric fields, we prove that, at half-filling, the ground state of the gauge theory coincides with the <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(\pi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>π</mi> </math></EquationSource> </InlineEquation>-flux phase, associated with magnetic flux equal to <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(\pi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>π</mi> </math></EquationSource> </InlineEquation> in every elementary lattice plaquette, provided the fermionic hopping is large enough. This proves in particular the semimetallic behavior of the ground state of the model. Furthermore, we compute the magnetic susceptibility of the gauge theory, and we prove that it is given by the one of massless 2<i>d</i> Dirac fermions, thus rigorously justifying recent numerical simulations. The proof is based on reflection positivity and chessboard estimates, and on lattice conservation laws for the computation of the transport coefficient.</p>

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Stability of the \(\pi \)-Flux Phase for \(\mathbb {Z}_{2}\) Lattice Gauge Theory Coupled to Fermionic Matter

  • 期刊论文

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  • 发表日期：

    2026年5月22日

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  • Leonardo Goller,
  • Marcello Porta

摘要

We consider the two-dimensional \(\mathbbm {Z}_{2}\) Z 2 lattice gauge theory coupled to fermionic matter. In absence of electric fields, we prove that, at half-filling, the ground state of the gauge theory coincides with the \(\pi \) π -flux phase, associated with magnetic flux equal to \(\pi \) π in every elementary lattice plaquette, provided the fermionic hopping is large enough. This proves in particular the semimetallic behavior of the ground state of the model. Furthermore, we compute the magnetic susceptibility of the gauge theory, and we prove that it is given by the one of massless 2d Dirac fermions, thus rigorously justifying recent numerical simulations. The proof is based on reflection positivity and chessboard estimates, and on lattice conservation laws for the computation of the transport coefficient.