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Mitas_QMC_Lab_notes

# Mitas_QMC_Lab_notes - Quantum Monte Carlo lab notes Lucas...

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Quantum Monte Carlo lab notes Lucas Wagner and Lubos Mitas August 8, 2006 1 DMC for Gaussian Wavefunctions Run the program by typing ~train18/mitas/dmc Here we’ll walk you through the usage of the simple DMC solver for the harmonic oscillator. The potential is 1 2 x 2 , so the exact energy is 0.5. The exact ground state wave function is proportional to e - 1 2 x 2 . By default, this program allows you to modify the exponent of the trial wave function and the timestep of the DMC simulation. No matter what you choose for the trial wave function, in the limit of zero time step, DMC will obtain 0.5 for the energy. The trial function only affects the efficiency of the simulation. This is in constrast to the many-fermion case, where fixed-node DMC will produce different results depending on the nodal surface of the trial function. We will not give you a tutorial, but more a list of things to try: Try entering 0.5 for the trial function parameter and any timestep (try 1.0). The average will be exactly 0.5 with zero error bar and there will be no timestep error. For a more realistic calculation, enter 0.6 for the trial function and several different timesteps (for example, 0.1, 0.05, 0.02, and 0.01). Plot the results and note the dependence on timestep and the extrapolation to zero. For those interested in the method, look into the code at ~train18/mitas/src/dmc_simple/dmc_simple.cpp There are many comments that explain how the method is implemented, and you can try an absolute value potential, the primitive propagator(which does not use a trial wave function), and many other things. If you are more interested in the practical use of a full-fledged code, look at the QWalk examples below, which show how we can calculate the total energy of chemical systems extremely accurately.

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