Condensed Matter Physics, 2009, vol. 12, No. 3, pp. 411428
DOI:10.5488/CMP.12.3.411
Title:
Highorder coupled cluster method calculations of spontaneous symmetry breaking in the spinhalf onedimensional J_{1}J_{2} 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 highorder coupled cluster method (CCM) calculations for "generalized" groundstate expectation values and the excited states of quantum magnetic systems with spin quantum number s ≥ 1/2. We use highorder CCM to demonstrate spontaneous symmetry breaking in the spinhalf J_{1}J_{2} 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 MajumdarGhosh point (J_{2}/J_{1}= 1/2) using a Néel model state. We show that the onset of dimerized phase is indicated by a bifurcation of the nearestneighbour ket and brastate correlation coefficients for the nearestneighbour Néel model state. We show that groundstate energies are in good agreement with the results of exact diagonalizations of finitelength chains across this entire regime (i. e., J_{1}>0 and J_{2} ≤ 1/2). The effects of the bifurcation point are also observed for the sublattice magnetization for the nearestneighbour model state. Finally, we use the new formalism for the excited state in order to obtain the excitation energy as a function of J_{2}/J_{1} for the nearestneighbour model state by solving up to the LSUB14 level of approximation. We obtain an extrapolated value for the excitedstate energy gap of 0.0036 at J_{2}/J_{1}=0.0 and of 0.2310 at J_{2}/J_{1}=0.5. We show that an excitation energy gap opens up at J_{2}/J_{1} ≈ 0.24, although the gap only becomes large at J_{2}/J_{1}≈ 0.4.
Key words:
highorder CCM, J_{1}J_{2} model, dimerization
PACS:
75.10.Jm, 75.10.Pq, 75.50.Ee
Comments: Figs. 7, Refs. 86, Tabs. 6
