Unconventional Phases in Doped or Frustrated Quantum Antiferromagnets

In present work, we apply state-of-the-art quantum Monte Carlo techniques, including the variational and the Green's function Monte Carlo with the fixed-node approximation, to investigate the ground-state properties of two strongly-correlated systems: the two-dimensional t-J model that can be used to study the high-temperature superconducting phase in the doped antiferromagnet, and the frustrated Neel antiferromagnet described by the J1-J2 Heisenberg model on the square lattice, which is widely considered as the prototype model for spin frustration.