论文标题
在二维价键实体中相互作用三倍的平均场理论：多层状态的稳定性和特性
Mean-field theory of interacting triplons in a two-dimensional valence-bond solid: stability and properties of many-triplon states
论文作者
论文摘要
我们研究了一种相互作用的三三角体（价值键固体的基本激发），该系统由键合形式中的有效相互作用的玻色子模型描述。特别是，我们考虑了方格旋转1/2 $ J_1 $ - $ J_2 $ ANTROMAGNETIC HEISENBERG模型，专注于中间参数区域，其中量子磁磁相集合，并考虑柱状柱价值 - 键键固体。在债券运营商理论中，Heisenberg模型就三胞胎操作员$ t $而言，将其映射到有效的玻色子模型中。在三胞胎运营商$ t $方面，研究了有效的玻色子模型，并以谐波近似和三倍的能量和三倍运营商的扩展进行了研究。这样的扩展使我们能够执行第二次映射，因此，根据三级操作员$ b $确定有效的相互作用的玻色子模型。然后，我们考虑具有固定数量三倍的系统，并确定平均场近似值内基本激发的基础激发频谱。我们表明，许多三极状态是稳定的，最低的能量是由少数三位符号组成的，并且激发差距是有限的。对于$ j_2 = 0.48 j_1 $和$ j_2 = 0.52 j_1 $，我们还计算自旋旋转和二聚体 - 二聚体相关函数，二聚体订单参数以及我们的均值形式中的双分部分von noumann纠缠熵，以确定许多tripliplon state act the triplon nork of Triplon nork的属性。我们发现自旋和二聚体相关性呈指数衰减，而纠缠熵遵守区域定律，无论三倍数字。此外，仅对于$ j_2 = 0.48 j_1 $，自旋相关性表明，具有较大三倍数字的多部门状态可能显示出比柱状价值键固体更均匀的单元图案。
We study a system of interacting triplons (the elementary excitations of a valence-bond solid) described by an effective interacting boson model derived within the bond-operator formalism. In particular, we consider the square lattice spin-1/2 $J_1$-$J_2$ antiferromagnetic Heisenberg model, focus on the intermediate parameter region, where a quantum paramagnetic phase sets in, and consider the columnar valence-bond solid phase. Within the bond-operator theory, the Heisenberg model is mapped into an effective boson model in terms of triplet operators $t$. The effective boson model is studied at the harmonic approximation and the energy of the triplons and the expansion of the triplon operators $b$ in terms of the triplet operators $t$ are determined. Such an expansion allows us to performed a second mapping, and therefore, determine an effective interacting boson model in terms of the triplon operators $b$. We then consider systems with a fixed number of triplons and determined the ground-state energy and the spectrum of elementary excitations within a mean-field approximation. We show that many-triplon states are stable, the lowest-energy ones are constituted by a small number of triplons, and the excitation gaps are finite. For $J_2=0.48 J_1$ and $J_2=0.52 J_1$, we also calculate spin-spin and dimer-dimer correlation functions, dimer order parameters, and the bipartite von Neumann entanglement entropy within our mean-field formalism in order to determine the properties of the many-triplon state as a function of the triplon number. We find that the spin and the dimer correlations decay exponentially and that the entanglement entropy obeys an area law, regardless the triplon number. Moreover, only for $J_2=0.48 J_1$, the spin correlations indicate that the many-triplon states with large triplon number might display a more homogeneous singlet pattern than the columnar valence-bond solid.
