High-order coupled cluster method calculations of spontaneous symmetry breaking in the spin-half one-dimensional J₁-J₂ model - Farnell, D.J.J. (Condensed Matter Physics, 2009)
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 = 1/2 ) using a N´eel 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 N´eel model state. We show that groundstate energies are in good agreement with the results of exact diagonalizations of nite-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 sublattice 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.