AI 中文总结
该研究采用矩阵乘积态张量网络方法，在AdS₂中标量φ⁴理论上提取边界谱、探测体临界性，确定了相变的临界指数等，表征了体与边界普适类。
AI 中文摘要
我们采用基于矩阵乘积态（matrix product states，MPS）的张量网络方法研究反德西特（anti-de Sitter，AdS）空间中的相互作用标量量子场论。我们开发了从全局AdS能级提取低能边界谱、通过AdS半径的有限尺寸标度探测体临界性以及识别共形边界条件的方法。将这些方法应用于AdS₂中的标量φ⁴理论，我们非微扰地计算了最低阶非平凡的ℤ₂-奇和偶边界标度维度，随后定位了体ℤ₂对称性破缺相变，并提取了与二维伊辛普适类一致的临界指数和中心电荷。在临界点处，我们确定了低能边界谱，并利用其识别出ℤ₂-守恒的自由/普通伊辛共形边界条件，从而同时表征了体和边界普适类。
英文摘要
We study interacting scalar quantum field theories in anti-de Sitter (AdS) space using a tensor-network approach based on matrix product states. We develop methods for extracting low-lying boundary spectra from global-AdS energy levels, probing bulk criticality through finite-size scaling in the AdS radius, and identifying conformal boundary conditions. Applying these methods to scalar $ϕ^4$ theory in $\mathrm{AdS}_2$, we compute the lowest non-trivial $\mathbb{Z}_2$-odd and even boundary scaling dimensions non-perturbatively. We then locate the bulk $\mathbb{Z}_2$ symmetry-breaking transition and extract critical exponents and central charge consistent with the 2D Ising universality class. At the critical point, we determine the low-lying boundary spectrum and use it to identify the $\mathbb{Z}_2$-preserving free/ordinary Ising conformal boundary condition, thereby characterising both the bulk and boundary universality classes.
Comments36 pages, 6 figures
