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Spin-Wave Theory on Finite Lattices: Application to the J1-J2 Heisenberg Model

We present a new method for a systematic spin-wave expansion for the quantum fluctuations of a generic spin Hamiltonian in a finite lattice, where the inverse spin magnitude 1/S is a well-defined expansion parameter. The first two leading contributions of the spin-spin correlation function are evaluated for the J1-J2 Heisenberg model. Very good agreement between our finite-size predictions and the exact diagonalization and Monte Carlo results is found for J2/J1 < 0.2 and S = 1/2, thus confirming the existence of antiferromagnetic long-range order in this J region. For J2/J1 > 0.3 the expansion is poorly converging, suggesting a possible breakdown of the spin-wave approximation. Here our calculation seems consistent with a possible spin liquid ground state.