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

We develop a generalization of the singlet sector valence bond basis projection 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 B750, 142 (2006); A. W. Sandvik and H. G. Evertz, arXiv:0807.0682, unpublished.) to cases in which the ground state of an antiferromagnetic Hamiltonian has total spin $S_{tot} = 1/2$ in a finite size system. We explain how various ground state expectation values may be calculated by generalizations of the estimators developed in the singlet case, and illustrate the power of the method by calculating the ground state spin texture and bond energies in a $L \times L$ Heisenberg antiferromagnet with $L$ odd and free boundaries.