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Photonic spin Hall effect (PSHE) in chiral PT-symmetric systems exhibits many exotic features, but the underlying physical mechanism has not been well elucidated. Here, through rigorous calculations based on full-wave theory, we reveal the physical mechanism of the exotic PSHE and identify a chirality-enabled topological phase transition. When circularly polarized light is incident on a chiral PT-symmetric system, the transmitted beam contains two components: a spin-flipped abnormal mode that acquires a geometric phase (exhibiting a vortex or a spin-Hall shift), and a spin-maintained normal mode that does not exhibit such a phase. If the phase difference between the cross-polarized Fresnel coefficients cannot be ignored, it results in a chirality-enabled phase and intensity distribution in the abnormal mode, which induces an exotic PSHE. Consequently, as the incident angle increases, a chirality-induced topological phase transition occurs, namely the transition from the vortex generation to the exotic PSHE. Finally, we confirm that the asymmetric and periodic PSHE in the chiral slab is also related to the phase difference between the cross-polarized Fresnel coefficients. These concepts and findings also provide an opportunity for unifying the phenomena of topological phase transitions in various spin-orbit photonic systems.

Changes of croplands often reflect the combined impacts of both natural environment changes and social agriculture activities. Such reflections manifested more significantly in agro-pastoral transition zones, e.g. in the North and West of China. In this study, cropland changes at the Yellow River–Huangshui River Valley, as a typical agro-pastoral transition zone in northwestern China, is analyzed in terms of the changes of the total amount and spatial pattern over the past 300 years (majorly in the Qing Dynasty). The reconstructed cropland data indicated a fluctuation of cropland areas in accordance with changes of regional climate conditions, natural hazards, agriculture activities and socio-economic development. A significant decrease of cropland in the middle of the 19th century was detected, which appeared a good consistency with the frequent natural disasters in the same period and the climate cooling trend across the whole 19th century. Though in the worsening conditions, three major copping strategies maintained and developed the local socio-agriculture system: (a) land reclamation policy encouraged immigrants and military farming; (b) construction of water conservancy facilities increased agricultural productivity; (c) increasing local Tibetans learned and transformed to implementing both agriculture and pastoral productions with flexibilities depending on climate conditions. The study demonstrates that the social-agriculture system held certain resilience, which can be maintained and enhanced with appropriate political, engineering, economic, and social-cultural measures.

The fully anisotropic two-leg spin- $\tfrac{1}{2}$ XXZ ladder model is studied in terms of an algorithm based on the tensor network (TN) representation of quantum many-body states as an adaptation of projected entangled pair states to the geometry of translationally invariant infinite-size quantum spin ladders. The TN algorithm provides an effective method to generate the groundstate wave function, which allows computation of the groundstate fidelity per lattice site, a universal marker to detect phase transitions in quantum many-body systems. The groundstate fidelity is used in conjunction with local order and string order parameters to systematically map out the groundstate phase diagram of the ladder model. The phase diagram exhibits a rich diversity of quantum phases. These are the ferromagnetic, stripe ferromagnetic, rung singlet, rung triplet, Néel, stripe Néel and Haldane phases, along with the two XY phases XY 1 and XY 2.