Generalization of the singlet sector valence-bond loop algorithm to antiferromagnetic ground states withtotal spin Stot = 1/2

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We develop a generalization of the singlet sector valence-bond basis projection algorithm ofSandvik, Beach, and Evertz (Sandvik 2005 Phys. Rev. Lett. 95 207203; Beach and Sandvik2006 Nucl. Phys. B 750 142; Sandvik and Evertz 2010 Phys. Rev. B 82 024407) to casesin which the ground state of an antiferromagnetic Hamiltonian has total spinStot = 1/2 in a finite-size system. We explain how various ground state expectation values may becalculated by using generalizations of the estimators developed in the singlet case, and illustratethe power of the method by calculating the ground state spin texture and bond energies in anL × L Heisenbergantiferromagnet with L odd and free boundaries.