Abstract
The coupled cluster method is implemented at high orders of approximation to investigate the zero-temperature (T = 0) phase diagram of the frustrated spin-s J1-J2-J3 antiferromagnet on the honeycomb lattice. The system has isotropic Heisenberg interactions of strength J1 > 0, J2 > 0 and J3 > 0 between nearest-neighbour, next-nearest-neighbour and next-next-nearest-neighbour pairs of spins, respectively. We study it in the case J3 = J2 ≡ κJ1, in the window 0 ≤ κ ≤ 1 that contains the classical tricritical point (at ) of maximal frustration, appropriate to the limiting value s → ∞ of the spin quantum number. We present results for the magnetic order parameter M, the triplet spin gap Δ, the spin stiffness ρs and the zero-field transverse magnetic susceptibility χ for the two collinear quasiclassical antiferromagnetic (AFM) phases with Néel and striped order, respectively. Results for M and Δ are given for the three cases , s = 1 and , while those for ρs and χ are given for the two cases and s = 1. On the basis of all these results we find that the spin- and spin-1 models both have an intermediate paramagnetic phase, with no discernible magnetic long-range order, between the two AFM phases in their T = 0 phase diagrams, while for s > 1 there is a direct transition between them. Accurate values are found for all of the associated quantum critical points. While the results also provide strong evidence for the intermediate phase being gapped for the case , they are less conclusive for the case s = 1. On balance however, at least the transition in the latter case at the striped phase boundary seems to be to a gapped intermediate state.
Highlights
Extended, uniform spin-lattice models of quantum magnets comprise a number N (! 1) of SU(2) spins with a given spin quantum number s placed on the sites of a specified regular, periodic lattice in d dimensions
coupled cluster method (CCM) is briefly reviewed in Sec. 3, before we present in Sec. 4 our results using it for the particular cases s = 1 and s =
In this case it has been explicitly shown [6] that the GS ordering has an infinitely degenerate family (IDF) of non-planar spin configurations, all degenerate in energy with the collinear striped states
Summary
Uniform spin-lattice models of quantum magnets comprise a number N (! 1) of SU(2) spins with a given spin quantum number s placed on the sites of a specified regular, periodic lattice in d dimensions. [33], but based only on calculations of the magnetic order parameter of the two AFM quasiclassical phases, the quantum phase diagram appears to be similar to the classical counterpart, i.e., with a direct first-order transition from the Neel to the striped phase, but with a critical value κc(s) slightly greater than κcl. The LSUBn ⌘ SUB2sn–n scheme is only equivalent to the SUBn–n scheme In any such scheme we utilize the (spaceand point-group) symmetries of both the system Hamiltonian and the CCM model state being used to reduce the set of independent multispin-flip configurations retained at any given order to a minimal number Nf. At a given nth level of LSUBn approximation, the number Nf = Nf (n) is lowest for s increases sharply as a function of s.
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