标题： 哈密顿量截断有效理论的系统改进 显示英文标题

标题： Systematic Improvement of Hamiltonian Truncation Effective Theory

摘要： 哈密顿截断有效理论是一种框架，旨在通过有效场论方法以系统的方式逐阶改进哈密顿截断的结果。 结果是一个带有修正项的截断有效哈密顿量，这些修正项来自于匹配过程。 我们通过计算在$1/E_{\rm max}$展开中的非平凡次领头阶修正来验证该方法的严谨性，其中$E_{\rm max}$是我们的有效理论截断。 我们通过 1+1D$\lambda \phi^4$理论明确地说明这一点，计算到阶数$1/E_{\rm max}^3$的修正。 在这个阶数下，必须包含对匹配条件的新非局部贡献。 我们证明，通过包括这些非局部项，误差按$1/E_{\rm max}^4$缩放，这符合有效场论的功率计数预期，提供了一个非平凡的检查，表明该方法是一致且稳健的。 我们还估计了该理论流到二维伊辛共形场论时的临界耦合，并确认尺度分离这一有效场论的基本特征在此阶数下仍然存在。 这些结果确立了哈密顿截断有效理论作为一种通用的、系统的框架，用于改进哈密顿截断的收敛性，并为将此方法应用于更高维的更复杂系统奠定了基础。 显示英文摘要

摘要： Hamiltonian Truncation Effective Theory is a framework that aims to improve the results of Hamiltonian truncation in a systematic, order-by-order fashion using Effective Field Theory methodology. The result is a truncated effective Hamiltonian with corrections that result from a matching procedure. We establish the rigor of this method by calculating nontrival next-to-leading order corrections in a $1/E_{\rm max}$ expansion, where $E_{\rm max}$ is our effective theory cutoff. We illustrate this explicitly using 1+1D $\lambda \phi^4$ theory, calculating corrections up to order $1/E_{\rm max}^3$. At this order, novel nonlocal contributions to the matching conditions must be incorporated. We show that by including these nonlocal terms, the error scales as $1/E_{\rm max}^4$, as expected from the Effective Field Theory power counting, providing a nontrivial check that this method is consistent and robust. We also estimate the critical coupling at which this theory flows to the 2D Ising conformal field theory and confirm that separation of scales, an essential feature of Effective Field Theory, persists at this order. These results establish Hamiltonian Truncation Effective Theory as a generic, systematic framework for improving convergence in Hamiltonian truncation and lay the groundwork to apply this method to more complex systems in higher dimensions.