Heisenberg antiferromagnet on a 1/7-depleted triangular lattice

Based on the triangular lattice and its depletions there are three simple f rustrated antiferromagnetic Heisenberg models in two dimensions. The first two, the triangular and kagome lattices, have been examined in the recent p ast. The triangular lattice seems to have a long range order whereas the ka gome does not show the long range order. But these results are still contro versial. This work is concentrated on a third type of this lattice family i n order to improve the understanding of the connection between the long ran ge order and coordination number in low dimensional systems. Bets has descr ibed the geometric properties of this lattice. It has a coordination number 5, which lies precisely between coordination numbers 6 and 4 of the other two lattices. The low-lying spectra and the correlation functions of finite lattices have been examined to discuss the possibility of a long range ord ered ground state in the 1/7-depleted triangular lattice. The low-lying spe ctrum is generated by an exact diagonalization, and the tower of states beh avior points to a long range ordered ground state.