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Diffusion Monte Carlo (DMC)

Diffusion Monte Carlo (DMC) is a projector method that extracts the ground state energy from a trial wavefunction by evolving it in imaginary time.

Overview

DMC solves the Schrödinger equation in imaginary time \(\tau = it\):

\[ -\frac{\partial \Psi}{\partial \tau} = (\hat{H} - E_T) \Psi \]

As \(\tau \to \infty\), the wavefunction projects onto the ground state \(\Phi_0\), provided the trial wavefunction \(\Psi_T\) has a non-zero overlap with \(\Phi_0\).

Key Features

  • Fixed-Node Approximation: To maintain the fermionic nature of the wavefunction (antisymmetry), the nodal surface is fixed to that of the trial wavefunction \(\Psi_T\). This provides a variational upper bound to the ground state energy.
  • Importance Sampling: The random walk is guided by the trial wavefunction to improve efficiency.
  • Time Step Error: The simulation uses a finite time step \(\tau\). Results should be extrapolated to \(\tau \to 0\).

Running DMC

DMC calculations are controlled by the blocking_dmc and dmc modules.

%module blocking_dmc
    dmc_nstep     100
    dmc_nblk      200
%endmodule

%module dmc
    tau           0.01
    etrial        -15.8
%endmodule

See Input Keywords for details.