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49149122483
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Due to the special form (point-like hybridization and coupling of the subsystems via spins only) of the interactions in Eq. 3, we can use the trivial redefinitions c1α (x) → c1α (x- Ri) to formally obtain x=0 as the impurity position in both of the leads.
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Due to the special form (point-like hybridization and coupling of the subsystems via spins only) of the interactions in Eq. 3, we can use the trivial redefinitions c1α (x) → c1α (x- Ri) to formally obtain x=0 as the impurity position in both of the leads.
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18
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The statement that the boundary condition representing the impurity-electron interaction in the TIKM is obtained by fusion with the Ising field σ is strictly speaking a hypothesis within BCFT, and as such must be tested against independent results. This was done in Ref. where it was shown that fusion with σ produces a finite-size spectrum in excellent agreement with numerical results for the TIKM.
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The statement that the boundary condition representing the impurity-electron interaction in the TIKM is obtained by fusion with the Ising field σ is strictly speaking a hypothesis within BCFT, and as such must be tested against independent results. This was done in Ref. where it was shown that fusion with σ produces a finite-size spectrum in excellent agreement with numerical results for the TIKM.
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19
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49149122979
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The boundary scaling dimensions Δn in the semi-infinite plane are connected to energy levels in a strip with the same boundary condition at the two edges. We are therefore effectively considering a finite-size energy spectrum with two quantum impurities present, one at each edge of the strip. Formally, this can be taken care of by performing fusion twice with σ× = σ (double fusion).
-
The boundary scaling dimensions Δn in the semi-infinite plane are connected to energy levels in a strip with the same boundary condition at the two edges. We are therefore effectively considering a finite-size energy spectrum with two quantum impurities present, one at each edge of the strip. Formally, this can be taken care of by performing fusion twice with σ× = σ (double fusion).
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The reason that L-1 does not contribute to the finite-temperature properties lies in the symmetry of the finite temperature geometry. The potential contributions of L-1 to the partition function are of the form 0β dτ L-1 (τ,0)... T, where the three dots in the correlator represent any other set of operators not depending on τ and the subscript T means that the correlator is evaluated in the finite-temperature geometry, i.e. a cylinder where τ=0 and τ=β are identified. Using L-1 (τ) = τ (τ) such terms are seen to vanish 0β dτ τ (τ,0)... = (β)...- (0)... = 0.
-
The reason that L-1 does not contribute to the finite-temperature properties lies in the symmetry of the finite temperature geometry. The potential contributions of L-1 to the partition function are of the form 0β dτ L-1 (τ,0)... T, where the three dots in the correlator represent any other set of operators not depending on τ and the subscript T means that the correlator is evaluated in the finite-temperature geometry, i.e. a cylinder where τ=0 and τ=β are identified. Using L-1 (τ) = τ (τ) such terms are seen to vanish 0β dτ τ (τ,0)... = (β)... - (0)... =0.
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22
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For an example of how the scaling fields in a BCFT formulation of a quantum impurity model depend on the microscopic parameters of the model (specifically the impurity valences)-as determined by an exact Bethe Ansatz solution-see Ref..
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For an example of how the scaling fields in a BCFT formulation of a quantum impurity model depend on the microscopic parameters of the model (specifically the impurity valences)-as determined by an exact Bethe Ansatz solution-see Ref..
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