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Though the potential is infinite ranged, it falls off quickly enough that the qualitative description is identical to that for short-ranged interactions (Ref.).
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The argument is as follows: we have lim ν′ → ν- Uc (qSS) (ν′) = Uc (CGS) (ν), as the state at filling ν-δ is the state at filling ν with a density δ of holelike solitons; as this density decreases a single particle added as a double occupancy will induce a charge configuration increasingly similar to that of forming a double occupancy in the half-filled state (which can be thought of as forming q holelike solitons by removing a single particle, then reinserting this particle as a double occupancy and letting the charge settle into its optimal distribution.) Further, the gap between Uc (qSS) (ν′) and UC (CGS) (ν′) vanishes as the denominator of the state ν′ goes to infinity, implying continuity of UC (CGS) from the left.
-
The argument is as follows: we have lim ν′ → ν- Uc (qSS) (ν′) = Uc (CGS) (ν), as the state at filling ν-δ is the state at filling ν with a density δ of holelike solitons; as this density decreases a single particle added as a double occupancy will induce a charge configuration increasingly similar to that of forming a double occupancy in the half-filled state (which can be thought of as forming q holelike solitons by removing a single particle, then reinserting this particle as a double occupancy and letting the charge settle into its optimal distribution.) Further, the gap between Uc (qSS) (ν′) and UC (CGS) (ν′) vanishes as the denominator of the state ν′ goes to infinity, implying continuity of UC (CGS) from the left.
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22
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73049114505
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The result is not monotonic in filling, as once at least half the sites are doubly occupied, the dipolar interaction of an extra double occupancy with the existing double occupancies becomes comparable to the energetic gain of creating holelike solitons in the CGS.
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The result is not monotonic in filling, as once at least half the sites are doubly occupied, the dipolar interaction of an extra double occupancy with the existing double occupancies becomes comparable to the energetic gain of creating holelike solitons in the CGS.
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24
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