Abstract:
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.