We summarize our theoretical findings on the ground-state phase diagram of the spin-½ XXZ chain having competing nearest-neighbor (J1) and antiferromagnetic next-nearest-neighbor (J2) couplings. Our study is mainly concerned with the case of ferromagnetic J1, and the case of antiferromagnetic J1 is briefly reviewed for comparison. The phase diagram contains a rich variety of phases in the plane of J1/J2 versus the XXZ anisotropy Δ: vector-chiral phases, Néel phases, several dimer phases, and Tomonaga–Luttinger liquid phases. We discuss the vector-chiral order that appears for a remarkably wide parameter space, successive Néel-dimer phase transitions, and an emergent nonlocal string order in a narrow region of ferromagnetic J1 side.
Abstract The square-lattice
J1 J 1 -
J2 J 2 XXZ model with the ring-exchange interaction K was investigated numerically. As for the hard-core-boson model with the nearest-neighbor hopping
J1/2 J 1 / 2 , namely, the
J1 J 1 -KXY model, it has been reported that the ring exchange leads to a variety of exotic phases such as the valence-bond-solid (VBS) phase. In this paper, we extend the parameter space to investigate the phase boundary between the XY (superfluid) and VBS phases. A notable feature is that the phase boundary terminates at the fully frustrated point,
J2/J1→0.5− J 2 / J 1 → 0 . 5 - . As a scaling parameter for the multi-criticality, the distance from the multi-critical point
δ(≥0) δ ( ≥ 0 ) is introduced. To detect the phase transition, we employed the high-order fidelity susceptibility
χF(3) χ F ( 3 ) , which is readily evaluated via the exact-diagonalization scheme. As a demonstration, for a fixed value of
δ δ , the XY-VBS criticality was analyzed by the probe
χF(3) χ F ( 3 ) . Thereby, with properly scaling
δ δ , the
χF(3) χ F ( 3 ) data were cast into the crossover-scaling formula to determine the multi-criticality. Graphic abstract
本文用两格点的量子关联研究无序系统的多体局域化相变。利用精确对角化的数值方法计算了无规磁场下自旋-1/2海森堡链的相邻本征态的两格点量子失谐之差与量子纠缠之差。结果表明在遍历相,相邻本征态的两格点量子失谐之差随链长的增长而逐渐趋近于零;而在多体局域化相,随链长的增长仍保持相对较大的值,这是多体局域化本征态违背本征态热化假定的反映,因此,相邻本征态的两格点量子失谐之差是研究多体局域化相变的有效工具。同时,与相邻本征态的两格点量子纠缠之差相比,分析发现用有限系统的量子失谐研究多体局域化相变比量子纠缠更具有优势。
Here we study the dimerized spin ladder with nearest-neighbor (J1) and next-nearest-neighbor (J2) anti-ferromagnetic interaction under a magnetic field. We predict the existence of different magnetization plateaus for the presence of spin-Peierls interaction on both J1 and J2. Magnetization plateau at m = 0 for J1 dimerization is spontaneous due to XY interaction, but it is absent for J2 dimerization, only intrinsic umklapp term leads to plateau (spin gap) state for some specific values of XXZ anisotropy (Δ) and J2. Here we predict a saturation plateau which is the classical phase of the system. There are some numerical support of our analytical approach already existing in the literature. The transition from commensurate gapped phase to incommensurate Luttinger liquid phase is the Mott-δ type of transition.
本文研究了具有两种三体相互作用的海森堡XXZ自旋链的量子相干与量子纠缠的特性。研究发现, 量子相干性不会出现突然死亡现象且非零量子相干性存在的温度范围大于量子纠缠存在的温度范围, 说明量子相干性相对于量子纠缠, 具有更强的鲁棒性。在量子临界环境中, 量子相干性可以表征本模型的量子相变现象。在铁磁情形中, 无论外磁场是否为0, 单独调控XZX+YZY三体相互作用对于减缓量子相干性的衰减速率与增大量子相干性存在的温度范围效果最好。在反铁磁情形中, 外磁场为0时, XZX+YZY与XZY-YZX两种三体相互作用的协同作用可以显著增加量子相干性的最大值, 并明显减缓其衰减速率。在铁磁情形与反铁磁情形中都发现当外磁场B<0时, 量子相干性存在的温度范围更大, 更有利于保存量子相干性。