Collinear antiferromagnetic phases of a frustrated spin-12 J1–

Abstract

The regions of stability of two collinear quasiclassical phases within the zerotemperature quantum phase diagram of the spin-1 2 J 1 -J 2 -J ⊥ 1 model on an AA-stacked bilayer honeycomb lattice are investigated using the coupled cluster method (CCM). The model comprises two monolayers in each of which the spins, residing on honeycomb-lattice sites, interact via both nearestneighbor (NN) and frustrating next-nearest-neighbor isotropic antiferromagnetic (AFM) Heisenberg exchange iteractions, with respective strengths J 1 > 0 and J 2 ≡ κJ 1 > 0. The two layers are coupled via a comparable Heisenberg exchange interaction between NN interlayer pairs, with a strength J ⊥ 1 ≡ δJ 1 . The complete phase boundaries of two quasiclassical collinear AFM phases, namely the Néel and Néel-II phases on each monolayer, with the two layers coupled so that NN spins between them are antiparallel, are calculated in the κδ half-plane with κ > 0. Whereas on each monolayer in the Néel state all NN pairs of spins are antiparallel, in the Néel-II state NN pairs of spins on zigzag chains along one of the three equivalent honeycomb-lattice directions are antiparallel, while NN interchain spins are parallel. We calculate directly in the thermodynamic (infinite-lattice) limit both the magnetic order parameter M and the excitation energy ∆ from the s z T = 0 ground state to the lowest-lying |s z T | = 1 excited state (where s z T is the total z component of spin for the system as a whole, and where the collinear ordering lies along the z direction), for both quasiclassical states used (separately) as the CCM model state, on top of which the multispin quantum correlations are then calculated to high orders (n ≤ 10) in a systematic series of approximations involving n-spin clusters. The sole approximation made is then to extrapolate the sequences of nth-order results for M and ∆ to the exact limit, n → ∞.

Frustrated spin-$\frac{1}{2}$ Heisenberg magnet on an $AA$-stacked honeycomb bilayer: High-order study of the collinear magnetic phases of the $J_{1}$--$J_{2}$--$J_{1}^{\perp}$ model

“…While the above (2m − 1)/2m staggering in LSUBn sequences of approximants for any physical quantity is common to all spin-lattice models on all lattices, honeycomb lattices tend to exhibit an additional (4m − 2)/4m staggering in the even subsequences, as has been noted elsewhere [22,24,58,65,89], and which now seems to originate in the non-Bravais nature of the honeycomb lattice [65], which itself comprises two interlacing triangular Bravais sublattices. Each of these displays the above-mentioned (2m − 1)/2m staggering, and the composite honeycomb lattice then magnifies the effect twofold into the observed (4m − 2)/4m staggering of the even (n = 2m) subsequence and, presumably, also a (4m − 3)/(4m − 1) staggering of the odd (n = 2m − 1) subsequence.…”

“…Thus, for example, the LSUBn approximants M (n) to the magnetic order parameter of strongly frustrated systems, particularly for those with a quantum phase transition between states with and without magnetic LRO, such as our present model, have been found (and see, e.g., Refs. [52,65,72,73,[84][85][86][87][88]) to be accurately fitted by the well tested extrapolation scheme…”

“…[18,23]). For this reason it is of considerable interest to investigate also the phase boundary of the Néel-II phase for the spin-1 2 J 1 -J 2 -J ⊥ 1 model on the honeycomb bilayer, which to our knowledge, has only been previously investigated [65] in the half-plane δ > 0, as also for the Néel phase. Again, to the best of our knowledge, there have been no prior investigations of the stability of both of these collinear magnetic orderings (i.e., Néel and Néel-II) on each monolayer of the bilayer model, in the case of ferromagnetic (FM) interlayer coupling (δ < 0), despite the fact that this case is particularly interesting in its own right, for reasons that we now elaborate.…”

Frustrated spin- 12 Heisenberg magnet on a square-lattice bilayer: High-order study of the quantum critical behavior of the J1−J2−J

“…Amongst many applications to quantum many-body problems in fields as diverse as nuclear physics, subnuclear physics, quantum chemistry, atomic and molecular physics, quantum optics, and condensed matter physics, the CCM has, in particular, by now been applied to a wide variety of spin-lattice systems of interest in quantum magnetism (see, e.g., Refs. [14,23,[25][26][27]33,35,50,82,83,85,107,108,111] and references therein). Since its application to such systems has already been widely described in the literature, therefore, we content ourselves here with presenting a brief overview of only those features that are most relevant to us now.…”

“…18, a well-tested scheme for systems with strong frustration, and/or for which the system has a QPT between states with and without magnetic LRO, has been found (see, e.g., Refs. [25][26][27]33,35,85,107,108,111] and references cited therein) to be given by…”