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We develop a generalization of the singlet sector valence bond basisprojection algorithm of Sandvik, Beach, and Evertz (A. W. Sandvik, Phys. Rev.Lett. 95, 207203 (2005); K. S. D. Beach and A. W. Sandvik, Nucl. Phys. B750,142 (2006); A. W. Sandvik and H. G. Evertz, arXiv:0807.0682, unpublished.) tocases in which the ground state of an antiferromagnetic Hamiltonian has totalspin $S_{tot} = 1/2$ in a finite size system. We explain how various groundstate expectation values may be calculated by generalizations of the estimatorsdeveloped in the singlet case, and illustrate the power of the method bycalculating the ground state spin texture and bond energies in a $L \times L$Heisenberg antiferromagnet with $L$ odd and free boundaries.

Generalization of the singlet sector valence bond loop algorithm to antiferromagnetic ground states with total spin $S_{tot}=1/2$