标题： 自旋-1/2 XX链与调制的Gamma相互作用 显示英文标题

标题： Spin-1/2 XX chains with modulated Gamma interaction

摘要： 我们研究了具有调制伽马相互作用（GI）的自旋-1/2 XX链，这来源于均匀和交替伽马项的叠加。 我们使用费米化技术精确对角化了该模型的哈密顿量。 然后我们探测能隙并确定有能隙和无能隙区域。 我们还检查了交替手性、交替尼美克和二聚序参数，以确定基态相图的不同相及其相应的长程序。 我们的研究结果表明，该模型经历了第一类、第二类、无能隙-无能隙和有能隙-有能隙相变。 显示英文摘要

摘要： We study the spin-1/2 XX chain with a modulated Gamma interaction (GI), which results from the superposition of uniform and staggered Gamma terms. We diagonalize the Hamiltonian of the model exactly using the Fermionization technique. We then probe the energy gap and identify the gapped and gapless regions. We also examine the staggered chiral, staggered nematic and dimer order parameters to determine the different phases of the ground state phase diagram with their respective long-range orders. Our findings indicate that the model undergoes first-order, second-order, gapless-gapless, and gapped-gapped phase transitions.