5 Hirsch-Fye quantum Monte Carlo method for ... - komet 337

5.22 Nils Blümer
1
0.8
0.6
Z
0.4
0.2
0
0.25
0.2
0.15
D
0.1
0.05
0
E
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
0 1 2 3 4 5 6
U
T=0.1
E pot
E tot
E kin
2OPT: T=0
Fig. 13: Quasiparticle weightZ (discrete estimate), double occupancyD, and energy contributions
for the 1-band Hubbard model on the Bethe lattice (bandwidthW = 4) at T = 0.1 in the
paramagnetic phase. Crosses (connected with lines) denote QMC results for∆τ = 0.2, squares
are for ∆τ = 0.125. For comparison, results of second order perturbation theory (2OPT) are
shown for the total energy and the double occupancy forT = 0 (solid black lines).
metal-insulator transition so that its interpretation as a quasiparticle weight breaks down. In
contrast, the discrete version (41) always leads to positive Z and may therefore appear more
physical. In any case, Z loses its theoretical foundation outside the Fermi liquid phase where
it remains only a heuristic indicator of a metal-insulator transition. In the uppermost part of
Fig. 13, Z is shown for the relatively high temperature T = 0.1. A rapid change of slopes
indicates a transition or crossover near U ≈ 4.7.
Energy
Within the DMFT, the energy per lattice site is given as [1, 8]
�
E = lim
η→0 +T
n,σ
� ∞
e
dǫ
iωnη ǫρ(ǫ)
iωn −ǫ−Σσ(iωn)
−∞
1 �
+ T Σσ(iωn)Gσ(iωn). (42)
2
n,σ