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

Abstract

The zero-temperature phase diagram of the spin-1 2 J 1-J 2-J ⊥ 1 model on an AA-stacked square-lattice bilayer is studied using the coupled cluster method implemented to very high orders. Both nearest-neighbor (NN) and frustrating next-nearest-neighbor Heisenberg exchange interactions, of strengths J 1 > 0 and J 2 ≡ κJ 1 > 0, respectively, are included in each layer. The two layers are coupled via a NN interlayer Heisenberg exchange interaction with a strength J ⊥ 1 ≡ δJ 1. The magnetic order parameter M (viz., the sublattice magnetization) is calculated directly in the thermodynamic (infinite-lattice) limit for the two cases when both layers have antiferromagnetic ordering of either the Néel or the striped kind, and with the layers coupled so that NN spins between them are either parallel (when δ < 0) or antiparallel (when δ > 0) to one another. Calculations are performed at nth order in a well-defined sequence of approximations, which exactly preserve both the Goldstone linked-cluster theorem and the Hellmann-Feynman theorem, with n 10. The sole approximation made is to extrapolate such sequences of nth-order results for M to the exact limit n → ∞. By thus locating the points where M vanishes, we calculate the full phase boundaries of the two collinear AFM phases in the κ-δ half-plane with κ > 0. In particular, we provide the accurate estimate (κ ≈ 0.547, δ ≈ −0.45) for the position of the quantum triple point (QTP) in the region δ < 0. We also show that there is no counterpart of such a QTP in the region δ > 0, where the two quasiclassical phase boundaries show instead an "avoided crossing" behavior, such that the entire region that contains the nonclassical paramagnetic phases is singly connected.

Two-triplon excitations of the Kitaev-Heisenberg-Bilayer

“…This case is of interest, as it provides additional insight into the qualitative picture for the occurrence of the ABS provided in the context of Eqs. ( 4) and (5).…”

“…Moreover, to lowest order, i.e., for J y,z = 0, the ABS (anti)binding energy is set by J x from Eqs. ( 4) and (5).…”

“…Tuning the interdimer exchange, these models allow for QPTs between states of weakly interacting singlets and various quantum phases determined by the type of interdimer network. Paradigmatic examples along this line include the square-lattice Heisenberg bilayer [2], three dimensional dimer networks [3], frustrated triangular and J 1 -J 2 Heisenberg bilayers [4,5], as well as the famous orthogonal dimer model [6]. Each of these models has been suggested to have corresponding realizations on the materials side, including BaCuSi 2 O 6 [7], TlCuCl 3 [8], Ba 3 Mn 2 O 8 [9], Li 2 VO(Si,Ge)O 4 [10], and SrCu 2 (BO 3 ) 2 [11], respectively.…”

Spectral characteristics of the antiferromagnetic spin-1/2 Heisenberg model on the square lattice in a magnetic field

“…The consideration of a two dimensional quantum antiferromagnet (2D-AFM) is usually based on various versions of the spin- 1 2 Heisenberg square-lattice model. This model continues to be studied [1,2,3,4,5,6,7,8]. It is used to describe superconducting cuprates and related compounds, including recently synthesized molecular 2D AFM [9,10,11,12].…”

Phase transition of spin-1 frustrated model on square-lattice bilayer

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理论上，对于一个考虑了层间耦合相互作用的 12cJ J J (这里 c J 是层间耦 合相互作用)模型是非常重要的.根据 Mermin-Wagner 定理 [7] ，各向同性的二维平 [11] 、 团簇平均场理论 [12] 和耦合团簇方法 [13] .这些研究都集中在其基态性质，对其在有 限温度时的研究非常有限.基于此，本文将聚焦其在有限温度的磁性质.鉴于实际 材料通常存在各向异性，模型引入了单离子各向异性 D .同时，注意到已有的研究 大多考虑层间耦合为反铁磁的情况 [9][10][11][12] ，对于其铁磁情况很少涉及 [13] ，本文将全 面考虑这两种层间耦合相互作用对系统相变的影响.结果显示：只要参数 c J 和 D 不同时为零，当 21 = / 2 JJ 时，AF1 态和 AF2 态具有相同的相变温度并且共存；当 21 /2 JJ  时，尽管 AF1-AF2 态有不同相变温度，但它们也可以共存.对于这两种

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