2017/08/31 by R. F. Bishop, P. H. Y. Li
Chemistry · Physics and Astronomy · #Advanced Condensed Matter Physics #Antiferromagnetism #Chemistry #Condensed matter physics #Crystallography #Lattice (music) #Order (exchange) #Phase (matter) #Phase diagram #Phase transition #Physics #Physics of Superconductivity and Magnetism #Quantum critical point #Quantum many-body systems #Quantum mechanics #Quantum phase transition #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.96.224416
published as Phys. Rev. B 96, 224416 (2017)
openalex created_date 2017/08/31 · arxiv created 2017/11/29 · openalex publication_date 2017/12/12 · arxiv updated 2017/12/20 · openalex updated_date 2026/08/05
We study a frustrated spin-(1)/(2)\phantom\rule0.16em0exJ1\text\ensuremath-J2\text\ensuremath-J3\text\ensuremath-J1^\ensuremath⊥ Heisenberg antiferromagnet on an AA-stacked bilayer honeycomb lattice. In each layer we consider nearest-neighbor (NN), next-nearest-neighbor, and next-next-nearest-neighbor antiferromagnetic (AFM) exchange couplings J1,\phantom\rule0.16em0exJ2, and J3, respectively. The two layers are coupled with an AFM NN exchange coupling J1^\ensuremath⊥\ensuremath≡\ensuremathδJ1. The model is studied for arbitrary values of \ensuremathδ along the line J3=J2\ensuremath≡\ensuremathαJ1 that includes the most highly frustrated point at \ensuremathα=(1)/(2), where the classical ground state is macroscopically degenerate. The coupled cluster method is used at high orders of approximation to calculate the magnetic order parameter and the triplet spin gap. We are thereby able to give an accurate description of the quantum phase diagram of the model in the \ensuremathα\ensuremathδ plane in the window 0\ensuremath≤\ensuremathα\ensuremath≤1,\phantom\rule0.16em0ex0\ensuremath≤\ensuremathδ\ensuremath≤1. This includes two AFM phases with N'eel and striped order, and an intermediate gapped paramagnetic phase that exhibits various forms of valence-bond crystalline order. We obtain accurate estimations of the two phase boundaries, \ensuremathδ=\ensuremathδ_ci(\ensuremathα), or equivalently, \ensuremathα=\ensuremathα_ci(\ensuremathδ), with i=1 (N'eel) and 2 (striped). The two boundaries exhibit an ``avoided crossing'' behavior with both curves being re-entrant. Thus, in this \ensuremathα\ensuremathδ window, N'eel order exists only for values of \ensuremathδ in the range \ensuremathδ_c1<(\ensuremathα)<\ensuremathδ<\ensuremathδ_c1>(\ensuremathα), with \ensuremathδ_c1<(\ensuremathα)=0 for \ensuremathα<\ensuremathα_c1(0)\ensuremath≈0.46(2) and \ensuremathδ_c1<(\ensuremathα)>0 for \ensuremathα_c1(0)<\ensuremathα<\ensuremathα1>\ensuremath≈0.49(1), and striped order similarly exists only for values of \ensuremathδ in the range \ensuremathδ_c2<(\ensuremathα)<\ensuremathδ<\ensuremathδ_c2>(\ensuremathα), with \ensuremathδ_c2<(\ensuremathα)=0 for \ensuremathα>\ensuremathα_c2(0)\ensuremath≈0.600(5) and \ensuremathδ_c2<(\ensuremathα)>0 for \ensuremathα_c2(0)>\ensuremathα>\ensuremathα2<\ensuremath≈0.56(1).