Destruction of Neel Ordering of S=1 Square Lattice Magnets

We introduce models of spin S=1 that can be simulated sign-problem free with means of a Stochastic Series Expansion Quantum Monte Carlo (SSE QMC). Compared to the S=1/2 case there is a plethora of new phases and phase transitions
that these models give access to. In this talk, we will focus on a spin-1 Heisenberg Model with both 2 and 4 spin bilinear-biquadratic interactions on the square lattice. We study the competion of Neel and valence bond solid phases and the nature of the quantum phase transitions between these states of matter.