Generalization of the singlet sector valence-bond loop algorithm to antiferromagnetic ground states with total spin S_tot = 1/2

Abstract

We develop a generalization of the singlet sector valence-bond basis projection algorithm of Sandvik, Beach, and Evertz (Sandvik 2005 Phys. Rev. Lett. 95 207203; Beach and Sandvik 2006 Nucl. Phys. B 750 142; Sandvik and Evertz 2010 Phys. Rev. B 82 024407) 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 using 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 an L × L Heisenberg antiferromagnet with L odd and free boundaries.