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We study two-dimensional Heisenberg antiferromagnets with additional multi-spin interactions which can drive the system into a valence-bond solid state. For standard SU(2) spins, we consider both four- and six-spin interactions. We find continuous quantum phase transitions with the same critical exponents. Extending the symmetry to SU(N), we also find continuous transitions for N=3 and 4. In addition, we also study quantitatively the cross-over of the order-parameter symmetry from Z4 deep inside the valence-bond-solid phase to U(1) as the phase transition is approached.
We consider the easy-plane limit of bipartite SU($N$) Heisenberg Hamiltonians which have a fundamental representation on one sublattice and the conjugate to fundamental on the other sublattice. For $N=2$ the easy plane limit of the SU(2) Heisenberg m
We calculate the bipartite von Neumann and second Renyi entanglement entropies of the ground states of spin-1/2 dimerized Heisenberg antiferromagnets on a square lattice. Two distinct dimerization patterns are considered: columnar and staggered. In b
We introduce a simple model of SO($N$) spins with two-site interactions which is amenable to quantum Monte-Carlo studies without a sign problem on non-bipartite lattices. We present numerical results for this model on the two-dimensional triangular l
We present the class of models of a nonmagnetic impurity in S=1/2 generalized ladder with an AKLT-type valence bond ground state, and of a S=1/2 impurity in the S=1 AKLT chain. The ground state in presence of impurity can be found exactly. Recently s
Every singlet state of a quantum spin 1/2 system can be decomposed into a linear combination of valence bond basis states. The range of valence bonds within this linear combination as well as the correlations between them can reveal the nature of the