1D valence bond solids in a magnetic field

A Valence bond solid (VBS) is a nonmagnetic, long-range ordered state of a quantum spin system where local spin singlets are formed in some regular pattern. We here study the competition between VBS order and a fully polarized ferromagnetic state as function of an external magnetic field in a one-dimensional extended Heisenberg model---the J-Q$_2$ model---using stochastic series expansion quantum Monte Carlo simulations with directed loop updates. We discuss the ground state phase diagram.