AI 中文总结
本研究在(1+1)维伊辛临界附近，通过哈密顿量截断和张量网络计算，证明介子谱存在通用质量标度，为解释相关准一维磁体激发提供了实用判据。
AI 中文摘要
在(1+1)维[(1+1)D]伊辛临界附近，磁扰动会诱导禁闭并产生一系列被称为介子的束缚态激发。本文表明，在对模型相关的微观耦合进行独立重标度后，这些介子具有通用的质量标度。稳定介子的数量由最轻的两介子阈值控制，而最轻介子的质量遵循由单一标度参数表征的连续轨迹。利用哈密顿量截断方法，我们在伊辛场论和近临界混合场伊辛链（MFIC）中数值得到了该轨迹。在重标度下，MFIC的轨迹和稳定介子计数的交叉窗口均与场论结果重合。为进一步证明介子谱的上述通用结构，我们研究了一类处于横向场下的四周期自旋-1/2海森堡-伊辛链，其参数空间包含一族量子伊辛临界点。该哈密顿量族包含准一维反铁磁体Ba(Sr)Co₂V₂O₈的有效自旋模型。利用张量网络计算，我们得到了BaCo₂V₂O₈对应的最轻介子质量轨迹，发现其也与场论结果给出的同一条通用曲线重合。我们的结果表明，量子伊辛临界的通用标度结构延伸至邻近的禁闭区域，支配了介子谱的组织，从而为解释超越E₈可积性的混合场下准一维伊辛类磁体的激发提供了实用判据。
英文摘要
Near $(1+1)$-dimensional [$(1+1)$D] Ising criticality, a magnetic perturbation induces confinement and produces a cascade of bound-state excitations known as mesons. Here we show these mesons share a universal mass scaling after independently rescaling the model-dependent microscopic couplings. The number of stable mesons is controlled by the lightest two-meson threshold, while the lightest-meson mass follows a continuous trajectory characterized by a single scaling parameter. Using Hamiltonian truncation method, we obtain the trajectory numerically in both Ising field theory and the near-critical mixed-field Ising chain (MFIC). Under the rescaling, the trajectory and stable-meson-count crossover windows of MFIC both collapse onto the field-theory results. To further demonstrate the above universal organization of the meson spectra, we consider a class of four-periodic spin-$1/2$ Heisenberg-Ising chains under transverse fields, whose parameter space contains a family of quantum Ising critical points. The Hamiltonian family includes effective spin models for the quasi-one-dimensional antiferromagnets Ba(Sr)Co$_2$V$_2$O$_8$. Using tensor-network calculations, we obtain the corresponding lightest-meson mass trajectory for BaCo$_2$V$_2$O$_8$ and find that it also collapse onto the same universal curve given by field-theory result. Our results suggest that the universal scaling structure of quantum Ising criticality extends into the nearby confining regime, governing the organization of the meson spectrum. They thereby provide a practical criterion for interpreting excitations of quasi-1D Ising-like magnets in mixed fields beyond $E_8$ integrability.
Comments7 pages, 4 figures
