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′, and the "cut" links, which corresponds to a particular gauge choice here.
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′, and the "cut" links, which corresponds to a particular gauge choice here.
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25
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77954827906
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After gauge fixing, the P̂ expansion of Ref. can be factorized: P̂ = [1+ Πi Di ] Ĝ = [1+ Pf ΠL Δ Φ] Ĝ, where Ĝ = [1+ Σj Dj + Σi
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After gauge fixing, the P ̂ expansion of Ref. can be factorized: P ̂ = [1 + Π i D i] G ̂ = [1 + P f Π L Δ Φ] G ̂, where G ̂ = [1 + Σ j D j + Σ i < j D i D j +] (note that D i 2 = 1).
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26
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77954831660
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This global flux operator can also be written in terms of spin variables along the global cycles (Refs.).
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This global flux operator can also be written in terms of spin variables along the global cycles (Refs.).
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27
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77954824644
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The exclusion of the (-1,-1 ) state from the ground state for g< gc is tied to the nA statistics of the vortices. A global flux threading Φα is equivalent to the procedure of (i) creating a vortex pair, (ii) transporting one vortex around the loop Γα, and (iii) annihilating the pair (Ref.). The (-1,-1 ) sector is equivalent to two vortex loops linked to each other, which cannot be undone in the nA phase.
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The exclusion of the (- 1, - 1) state from the ground state for g < g c is tied to the nA statistics of the vortices. A global flux threading Φ α is equivalent to the procedure of (i) creating a vortex pair, (ii) transporting one vortex around the loop Γ α, and (iii) annihilating the pair (Ref.). The (- 1, - 1) sector is equivalent to two vortex loops linked to each other, which cannot be undone in the nA phase.
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77954832730
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(private communication).
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