High-order coupled cluster method calculations of spontaneous symmetry breaking in the spin-half one-dimensional J1-J2 model

In this article we present new formalism for high-order coupled cluster method (CCM) calculations for "generalized" ground-state expectation values and the excited states of quantum magnetic systems with spin quantum number s ≥ 1/2 We use high-order CCM to demonstrate spontaneous symmetry breaking in the spin-half J1-J2 model for the linear chain using the coupled cluster method (CCM). We show that we are able to reproduce exactly the dimerized ground (ket) state at the Majumdar-Ghosh point (J2/J1 = 12) using a Néel model state. We show that the onset of dimerized phase is indicated by a bifurcation of the nearest-neighbour ket and bra-state correlation coefficients for the nearest-neighbour Néel model state. We show that ground- state energies are in good agreement with the results of exact diagonalizations of finite-length chains across this entire regime (i. e., J1 > 0 and J2 ≤ 1/2). The effects of the bifurcation point are also observed for the sub- lattice magnetization for the nearest-neighbour model state. Finally, we use the new formalism for the excited state in order to obtain the excitation energy as a function of J2/J1 for the nearest-neighbour model state by solving up to the LSUB14 level of approximation. We obtain an extrapolated value for the excited-state energy gap of -0.0036 at J2/J1 = 0.0 and of 0.2310 at J2/J1 = 0.5. We show that an excitation energy gap opens up at J2/J1 ≈ 0.24, although the gap only becomes large at J2/J1 ≈ 0.4. © D.J.J. Farnell.