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Auxiliary field Monte-Carlo for quantum many-body ground states

1986; Elsevier BV; Volume: 168; Issue: 1 Linguagem: Inglês

10.1016/0003-4916(86)90107-7

1096-035X

G Sugiyama, S. E. Koonin,

Physics of Superconductivity and Magnetism

We develop an algorithm for determining the exact ground state properties of quantum many-body systems which is equally applicable to bosons and fermions. The Schroedinger eigenvalue equation for the ground state energy is recast as a many-dimensional integral using the Hubbard-Stratonovitch representation of the imaginary-time many-body evolution operator. The integral is then evaluated stochastically. We test the algorithm for an exactly soluble boson system with an attractive potential and then extend it to fermions and repulsive potentials. Importance sampling is crucial to the success of the method, particularly for more complex systems. Computational efficiency is improved by performing the calculations in Fourier space.