2.6M - 1. Institut für Theoretische Physik - Universität Stuttgart

Initialisation (VQMC, see figure 2.1)
b = 0
b ↦→ b + 1
Generate random numbers: �η, X , ζ
�F ( � R) = Re � ∇ΨG(�R)
ΨG(�R)
�R ′ = � R + ∆τ � F ( � R) + �η
W ( � R ′ , � R; ∆τ) = |ΨG(�R ′ )| 2 ˜GD(�R,�R ′ ;∆τ)
|ΨG(�R)| 2 ˜GD(�R ′ ,�R;∆τ)
Paccept( � R, � R ′ ; ∆τ) > X ?
Yes No
m = 1 m = 0
�R ↦→ � R ′
∅
EL( � R ′ ) = ˆH ΨG(�R ′ )
ΨG(�R ′ )
τ ↦→ τ + ∆τ
ϕ = e i∆τ Im EL(�R ′ ) , Υ(s)
m = 1?
Yes No
¯PB = int(e−∆τ(Re EL(�R ′ )−ET) + ζ)
PB
¯ = int(0.9 + ζ)
¯PB = 1?
Yes No
¯PB = 0?
∅
Delete walker
j max ↦→ j max − 1
EL(s) =
Yes No
Pjmax j
j =1 EL (�R ′ )·Υj (s)
Pjmax j =1 Υj (s)
�R ′ ↦→ � R
All steps of each block (s = 1 . . . smax)? EB(b) = 1 �smax smax s=1 EL(s)
ET = 1
2 (ET + 1 �
b b EB(b))
Renormalise the number of walkers
All blocks (b = 1 . . . bs . . . bmax)?
�bmax E0 =
b=bs EB(b)
1
b max−bs+1
Copy walker
j max ↦→ j max +max( ¯ PB, 2)
Figure 1.: Nassi-Shneiderman diagram of the DQMC method.
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