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High-order coupled cluster method calculations of spontaneous symmetry breaking in the spin-half one-dimensional J(1)-J(2) model

Farnell, Damian J. J. 2009. High-order coupled cluster method calculations of spontaneous symmetry breaking in the spin-half one-dimensional J(1)-J(2) model. Condensed Matter Physics 12 (3) , pp. 411-428. 10.5488/CMP.12.3.411

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Abstract

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.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Dentistry
Subjects: Q Science > QC Physics
Uncontrolled Keywords: high-order CCM, J1-J2 model, dimerization
Publisher: Institute for Condensed Matter Physics
ISSN: 1607-324X
Last Modified: 04 Jun 2017 06:23
URI: http://orca.cf.ac.uk/id/eprint/59352

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