论文标题

在横向iSing模型中解剖量子相变

Dissecting Quantum Phase Transition in the Transverse Ising Model

论文作者

Yang, Yun-Tong, Chen, Fu-Zhou, Luo, Hong-Gang

论文摘要

尽管通过重新归一化的群体理论建立了对与相变有关的关键现象的完整理论描述,但相变的微观性质仍然令人满意地理解。例如,个体之间的相互作用如何将系统从一个阶段驱动到另一个阶段,因为特定参数会有所不同,并且个人在此过程中如何响应该参数的变化?在这里,我们以一维横向ISING模型(TIM)中研究良好的量子相变(QPT)为示例,以展示这种微观过程。 We first introduce $2L$ collective structures,referred to as patterns, for the TIM with $L$ ferromagnetically interacting spins, and then analyze the contributions of these patterns to the system's states, e.g., the ground state, the first excited state, and so on, from which the analogue of the QPT process between the disordered phase in the weakly coupling regime and the ferromagnetic phase in the strongly coupling regime is围绕交互强度明确识别$ j_c = 1 $。我们系统地探索了$ l = 6、8、10、12 $的小晶格大小的过程,其基态能量与直接数值精确的对角度相同。将系统尺寸提高到$ L = 128 $,逐渐接近热力学限制的实际QPT点。我们的结果表明,模式图片不仅能够提供相变的微观过程,而且还具有分析QPT在不同量子模拟平台中的类似物中的实际兴趣。

Despite the fact that a complete theoretical description of critical phenomena in connection with phase transitions has been well-established through the renormalization group theory, the microscopic nature of the phase transitions remains to be understood in a satisfactory way. For example, how does the interaction between individuals drive a system from one phase to another as a specific parameter varies, and how do the individuals respond to changes in this parameter during the process? Here we take the well-studied quantum phase transition (QPT) in the one-dimensional transverse Ising model (TIM) as an example to exhibit such a microscopic process. We first introduce $2L$ collective structures,referred to as patterns, for the TIM with $L$ ferromagnetically interacting spins, and then analyze the contributions of these patterns to the system's states, e.g., the ground state, the first excited state, and so on, from which the analogue of the QPT process between the disordered phase in the weakly coupling regime and the ferromagnetic phase in the strongly coupling regime is clearly identified around the interaction strength $J_c =1$. We systematically explore this process for small lattice sizes of $L=6, 8, 10, 12$, whose ground state energies are identical to those obtained by direct numerical exact diagonalization. Increasing the system size up to $L=128$, the actual QPT point located at $J_c = 1$ in the thermodynamical limit is gradually approached. Our results show that the pattern picture is not only able to provide a microscopic process of phase transitions, but also of practical interest in analyzing analogues of QPT in diverse quantum simulation platforms.

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