Valence-bond-solid phases and quantum phase transitions in two-dimensional antiferromagnets

  Anders W. Sandvik Boston University

  A two dimensional antiferromagnet with Heisenberg interactions J*Si*Sj between nearest neighbor spins on a square lattice has long-range Neel order in the ground state. Including other interactions, different types of nonmagnetic ground states are also possible. Such states, and the associated quantum phase transitions from the Neel state, have been actively investigated during the past two decades. However, unbiased numerical studies of model hamiltonians expected to exhibit these phases and transitions have been hampered by the "sign problem" affecting quantum Monte Carlo simulations of frustrated spin models. I will discuss two models for which it turns out to be possible to study transitions from the Neel state into valence bond solids phases: O(1) and SU(2) symmetric models including particular types of four-spin interactions. In the SU(2) case, simulations are possible by using the valence bond basis. Preliminary results indicate a continuous quantum phase transition which may be in the universality class of the recently proposed "deconfined" quantum critical point. The transition in the O(1) model is also unusual but does not fit within the deconfined quantum-criticality scenario.