Quantum Monte Carlo scheme for frustrated Heisenberg antiferromagnets

When one tries to simulate quantum spin systems by the Monte Carlo method, often the ‘minus-sign problem’ is encountered. In such a case, an application of probabilistic methods is not possible. In this paper the method has been proposed how to avoid the minus sign problem for certain class of frustrated Heisenberg models. The systems where this method is applicable are, for instance, the pyrochlore lattice and the $J_1-J_2$ Heisenberg model. The method works in singlet sector. It relies on expression of wave functions in dimer (pseudo)basis and writing down the Hamiltonian as a sum over plaquettes. In such a formulation, matrix elements of the exponent of Hamiltonian are positive.