标题： 量子伊辛阶梯中的介子 显示英文标题

标题： Mesons in a quantum Ising ladder

摘要： 当两个具有磁序的横向场伊辛链（TFICs）耦合时，原来的自由激发变得被约束，产生类似介子的束缚态。 在本工作中，我们系统地研究了这些束缚态。 这些介子通过它们的费米子数奇偶性和链交换特性来表征，这导致了不同的介子态集合。 介子质量是通过求解贝特-萨珀方程来确定的。 一个有趣的观察是，在链交换奇数区中存在额外的简并。 除了两粒子近似之外，我们利用截断的自由费米子空间方法进行数值计算以得到谱。 得到了介子质量的修正，并进一步确认了简并性。 这种表征和简并性可以与每个链被调谐到量子临界的情况相联系，在这种情况下，系统由伊辛$_h^2$可积模型描述，这是一种带有$\mathbb{Z}_2$轨形的正弦-戈登理论。 在这里，我们建立了玻色化形式中的粒子与其费米子对应物之间的清晰对应关系。 在此点附近，使用形式因子微扰方案分析了这些粒子的稳定性，其中始终存在四个粒子。 此外，我们计算了局部自旋算符的主要动力学结构因子的演化，为低能激发及其在系统行为中的作用提供了进一步的见解。 两粒子约束框架以及奇偶性分类可能启发对其他耦合双部分系统的研究所。 显示英文摘要

摘要： When two transverse-field Ising chains (TFICs) with magnetic order are coupled, the original free excitations become confined, giving rise to meson-like bound states. In this work, we study such bound states systematically. The mesons are characterized by their fermion number parity and chain-exchanging properties, which lead to distinct sets of mesonic states. The meson masses are determined by solving the Bethe-Salpter equation. An interesting observation is the additional degeneracy in the chain-exchanging odd sectors. Beyond the two particle approximation, we exploit the truncated free fermionic space approach to calculate the spectrum numerically. Corrections to the meson masses are obtained, and the degeneracy is further confirmed. The characterization and degeneracy can be connected to the situation when each chain is tuned to be quantum critical, where the system is described by the Ising$_h^2$ integrable model, a sine-Gordon theory with $\mathbb{Z}_2$ orbifold. Here we establish a clear correspondence between the particles in the bosonized form and their fermionic counterparts. Near this point, the stability of these particles is analyzed using the form factor perturbation scheme, where four particles are always present. Additionally, we calculate the evolution of the dominant dynamical structure factor for local spin operators, providing further insight into the low-energy excitations and their role in the system's behavior. The two-particle confinement framework as well as the parity classifications may inspire the study for other coupled bi-partite systems.