Quantum phase transitions studies of some low-dimensional exactly solvable dimerized quantum antiferromagnets

Quantum fluctuations play very crucial role in low-dimensional
frustrated antiferromagnets. As a result, the magnetic ordered ground
state of a system becomes unstable and a quantum paramagnetic state
emerges as the ground state. An ordered state is also influenced by
the frustration which arises from the competing interactions present
on the lattice geometry. Quantum fluctuations and frustration together
give many novel quantum paramagnetic phases such as valence bond
crystal, spin-liquid phases. In this talk, I will present quantum
phase transitions studies of certain quantum antiferromagnetic spin
models in 2D which show spontaneously dimerized valence bond crystal
ground states. An important feature of these models is that these are
exactly solvable at some special limits.