| The ordinary Heisenberg model that possesses the SU(2) symmetry can easily be generalized to higher symmetry simply by regarding a symbol "S" in the Heisenberg Hamiltonian as a generator of the SU(N) instead of SU(2). Here we concentrate on the two-dimensional model with symmetric representations, namely, the cases where an SU(N) spin can be expressed as a small number of, say M, bosons with N types. Besides possible connections to electron systems with orbital degeneracy, this model is interesting for several reasons. For example, it is theoretically predicted that, depending on the value of M and N, the SU(N) Heisenberg model may exhibit a quantum disordered state as well as various ground states with non-trivial spatial structures, such as the dimerized state and the striped state. From quantum Monte Carlo simulation, we find that it is indeed true for M=1 but only for N<=5 where spontaneous dimerization can be observed. The case of M>1 and the possibility of the disordered ground state are also discussed. |
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