Magnetic Field Induced Semimetal-to-Canted-Antiferromagnet ...

6 Results
1/L Sqrt
0.25
0.2
0.15
0.1
0.05
Mz=0
0
0 1 2 3 4 5
U/t
10x10
12x12
14x14
m x,MF
Figure 6.2: Staggered magnetization and the mean field parameter mx,MF vs. interaction strength
U. For comparison, mean-field data is plotted.
particle via 〈ĉk,σ(τ)ĉ †
k,σ 〉 eperimentally corresponds to inverse photoemission spectroscopy
(IPES). Likewise photoemission spektroscopy (PES) yields information about the occupied
band structure below the chemical potential. In case of half filling Gk,σ and Gk,σ are linked
via a particle-hole transformation. The condition of half-filling reads
�
σ
〈ĉ †
i,σ ĉi,σ〉 = 1 . (6.6)
and thus fixes the number of electrons per site to one. On bipartite lattices this im-
plies the invariance of the Hubbard Hamiltonian, H = HT + HU under a particle-hole-
transformation which is defined as
ĉi,σ → ηiĉ †
i,−σ , (6.7)
with ηi = ±1 for i ∈ A, B. This takes â↑ to â †
is transformed like
Gk,σ(τ) =
p−h−transf.
1
N 2
�
i,j
1
= ηiηj
N 2
�
↓ and ˆb↑ to -ˆb †
↓
〈ĉi,σ(τ)ĉ †
j,σ 〉e−ık(i−j)
i,j
〈ĉ †
−ık(i−j)
i,−σ
(τ)ĉj,−σ〉e
. The Green function Gk,σ(τ)
(6.8)
Thus, the Green function being a 2 × 2-matrix, acquires a minus sign only on the off-
diagonal elements that is if i and j belong to different sublattices.
In short this means to study Gk,↑(τ) = 〈ĉ †
k,↑ (τ)ĉk,↑〉 one only has to look at
Gk,↓(τ) = 〈ĉk,↓(τ)ĉ †
k,,↓ 〉.
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