High-order coupled cluster method calculations of spontaneous symmetry breaking in the spin-half one-dimensional J_{1}-J_{2} model

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 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 Majumdar-Ghosh 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 nearest-neighbour ket-and bra-state correlation coefficients for the nearest-neighbour Néel model state. We show that groundstate energies are in good agreement with the results of exact diagonalizations of finite-length 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 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 J 2 /J 1 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 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.

Analytical and numerical studies of the one-dimensional sawtooth chain

“…4. Similar to previous research [25], we found that the results for the extrapolation of LSUBn data are not accurate in the region where c1 α α ≈ . So, the spin gap obtained from CCM is not displayed in Fig.…”

“…In Refs. [24,25], it was shown that CCM can be used to analyze the dimer and plaquette valence-bond phases of quantum spin systems perfectly. Here, we also apply CCM to the study of the dimerized state of the sawtooth chain.…”

The spin-1/2 square-lattice J1-J2 model: the spin-gap issue

“…The LSUBn approximation becomes exact for n → ∞, and so we can improve our results by extrapolating the "raw" LSUBn data to n → ∞. There are well-tested extrapolation rules [15,19,20,46,47,[51][52][53][54][56][57][58][59][60] for the ground-state energy per spin e GS = E GS (n)/N, the magnetic order parameter m s (n), and the spin gap ∆ e (n). We use e GS (n) = a 0 + a 1 (1/n) 2 + a 2 (1/n) 4 for the ground-state energy, m s (n) = b 0 + b 1 (1/n) 1/2 + b 2 (1/n) 3/2 for the magnetic order parameter, and ∆ e (n) = c 0 + c 1 (1/n) + c 2 (1/n) 2 for the spin gap.…”

“…It was found in Refs. [46] and [47] that the opening of the spin gap at the transition point to the valence-bond phase is well described by the CCM.…”

“…[43] The spin gap can be calculated directly within the framework of the CCM by using an appropriate excited-state formalism. [44][45][46][47] 2 Brief illustration of the coupled-cluster method…”