Projector Quantum Monte Carlo without minus-sign problem

Hans‐Georg Matuttis, Nobuyasu Ito

The quantum Monte Carlo method for the Hubbard model using the Hubbard-Stratonovich transformation is reexamined. It is observed that the value of the ground state energy for a 3×2 and 4×4 system is estimated correctly by ignoring the minus-sign of the negative sampling weight appearing in the simulation using the projector method. It is also observed that the average of sign is positive and the correlation between the energy and the sign is weak for these systems. The reasons why the ground state energy is estimated correctly is given on a phenomenological base.

Marjan Maček, Philipp T. Dumitrescu, Corentin Bertrand +3 more

Johan Nilsson

A. Muramatsu, Gil Zumbach, X. Zotos

It is shown that the sign of the fermionic determinant in the projector Monte Carlo method is directly related to a topological invariant. A key ingredient to obtain this result is the identification of the appropriate manifolds to describe the evolution of a fermionic trial wavefunction. They allow for a purely geometrical consideration of the minus-sign problem.

Hans A. De Raedt, Wolfgang von der Linden

Existing quantum Monte Carlo algorithms suffer the so-called minus-sign problem. We propose a stochastic algorithm to compute ground-state properties of quantum lattice models that is free of minus-sign problems. Illustrative results for the two-dimensional Hubbard model are presented.

P. Pitanga, Kleber Carlos Mundim