Title: High-order coupled cluster method calculations of spontaneous symmetry breaking in the spin-half one-dimensional J₁-J₂ model
Author(s):

D.J.J. Farnell (Academic Department of Radiation Oncology, Faculty of Medical and Human Science, University of Manchester, c/o The Christie NHS Foundation Trust M20 4BX, Manchester, United Kingdom)

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 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 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.

Key words: high-order CCM, J₁-J₂ model, dimerization
PACS: 75.10.Jm, 75.10.Pq, 75.50.Ee
Comments: Figs. 7, Refs. 86, Tabs. 6

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