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Update PDMC algorithm

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Anthony Scemama 2021-02-02 17:04:18 +01:00
parent b63191f9a7
commit d3d1e84680
1 changed files with 12 additions and 11 deletions
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@ -2392,18 +2392,19 @@ gfortran hydrogen.f90 qmc_stats.f90 vmc_metropolis.f90 -o vmc_metropolis
where $\mathbf{r}_i$ are the coordinates along the trajectory and we introduced a time-step $\delta t$. where $\mathbf{r}_i$ are the coordinates along the trajectory and we introduced a time-step $\delta t$.
The algorithm can be rather easily built on top of your VMC code: The algorithm can be rather easily built on top of your VMC code:
1) Compute a new position $\mathbf{r'} = \mathbf{r}_n + 0) Start with $W=1$
1) Evaluate the local energy at $\mathbf{r}_{n}$ and accumulate it
2) Compute the weight $w(\mathbf{r}_n)$
3) Update $W$
4) Compute a new position $\mathbf{r'} = \mathbf{r}_n +
\delta t\, \frac{\nabla \Psi(\mathbf{r})}{\Psi(\mathbf{r})} + \chi$ \delta t\, \frac{\nabla \Psi(\mathbf{r})}{\Psi(\mathbf{r})} + \chi$
5) Evaluate $\Psi(\mathbf{r}')$ and $\frac{\nabla \Psi(\mathbf{r'})}{\Psi(\mathbf{r'})}$ at the new position
Evaluate $\Psi$ and $\frac{\nabla \Psi(\mathbf{r})}{\Psi(\mathbf{r})}$ at the new position 6) Compute the ratio $A = \frac{T(\mathbf{r}' \rightarrow \mathbf{r}_{n}) P(\mathbf{r}')}{T(\mathbf{r}_{n} \rightarrow \mathbf{r}') P(\mathbf{r}_{n})}$
2) Compute the ratio $A = \frac{T(\mathbf{r}_{n+1} \rightarrow \mathbf{r}_{n}) P(\mathbf{r}_{n+1})}{T(\mathbf{r}_{n} \rightarrow \mathbf{r}_{n+1}) P(\mathbf{r}_{n})}$ 7) Draw a uniform random number $v \in [0,1]$
3) Draw a uniform random number $v \in [0,1]$ 8) if $v \le A$, accept the move : set $\mathbf{r}_{n+1} = \mathbf{r'}$
4) if $v \le A$, accept the move : set $\mathbf{r}_{n+1} = \mathbf{r'}$ 9) else, reject the move : set $\mathbf{r}_{n+1} = \mathbf{r}_n$
5) else, reject the move : set $\mathbf{r}_{n+1} = \mathbf{r}_n$
6) evaluate the local energy at $\mathbf{r}_{n+1}$
7) compute the weight $w(\mathbf{r}_i)$
8) update $W$
Some comments are needed: Some comments are needed: