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 (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 B750, 142 (2006); A. W. Sandvik and H. G. Evertz, arXiv:0807.0682, unpublished.)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.

6 pages, 6 figures

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• Properties of the random-singlet phase: from the disordered Heisenberg chain to an amorphous valence-bond solid
• Quantum Monte Carlo studies of spinons in one-dimensional spin systems
• Vacancy-induced spin texture in a one dimensional $S=1/2$ Heisenberg antiferromagnet
• Impurity spin texture at a Néel-Valence Bond Solid critical point in $d=2$ SU(3) quantum antiferromagnets
• Resonating valence bond trial wave functions with both static and dynamically determined Marshall sign structure
• Correlated valence-bond states
• Dulmage-Mendelsohn percolation: Geometry of maximally-packed dimer models and topologically-protected zero modes on site-diluted bipartite lattices
• Antiferromagnetic order in systems with doublet $S_{\mathrm{tot}}=1/2$ ground states
• Class of variational ansaetze for the "spin-incoherent" ground-state of a Luttinger liquid coupled to a spin bath
• Magnetic effects of non-magnetic impurities in gapped short-range resonating valence bond spin liquids
• Valence-Bond Quantum Monte Carlo Algorithms Defined on Trees