Simulating finite-momentum states of quantum spin systems in the valence bond basis

Quantum spin systems such as the Heisenberg model can be simulated numerically in the valence bond basis, as an alternative to the standard basis of eigenstates of the $S^z_i$ operators [1]. One advantage of this approach is that also the triplet sector can be studied based on the configurations generated in the singlet sector [1,2]. This way an improved estimator for the singlet-triplet gap can be constructed. Here we show that also finite-momentum triplet states can be studied [in practice for $q$ close to $0$ or $\mathbf{\pi}$ due to a phase problem], thus allowing us to calculate the triplet dispersion $E(q)$. Matrix elements $\langle T(q)|S^z_q|0\rangle$ are also accessible. These matrix elements give directly the magnon weight in the dynamic structure factor $S(q,\omega)$. We also discuss how deconfined spinon excitations can be detected in this approach. \hskip10.5cm [1] A. W. Sandvik, Phys. Rev. Lett. \textbf{95}, 207203 (2005).\hfill\break [2] K. S. D. Beach and A. W. Sandvik, Nucl. Phys. B \textbf{750}, 142 (2006).