强耦合量子场论中次首阶重正化哈密顿截断的高精度计算
High-Precision Calculations in Strongly Coupled Quantum Field Theory with Next-to-Leading-Order Renormalized Hamiltonian Truncation
摘要：
哈密顿截断（Hamiltonian Truncation）截断谱方法是求解d=2维时空中强耦合QFT的一种有效的数值方法。需要进一步的理论发展，以提高其准确性和适用范围。考虑到这一目标，在这里，我们提出了一个新的变体的哈密顿截断表现出更小的依赖于UV截止比其他现有的实现，并产生更准确的光谱。实现这一目标的关键思想在于精确地积分出某类高能态，这对应于在相互作用强度的立方阶进行重整化。我们测试的强耦合的二维四次标量理论的新方法。我们的工作也将有助于未来的目标扩展到更高的维d >= 3的哈密顿截断。
英文摘要：
Hamiltonian Truncation (a.k.a. Truncated Spectrum Approach) is an efficient numerical technique to solve strongly coupled QFTs in d=2 spacetime dimensions. Further theoretical developments are needed to increase its accuracy and the range of applicability. With this goal in mind, here we present a new variant of Hamiltonian Truncation which exhibits smaller dependence on the UV cutoff than other existing implementations, and yields more accurate spectra. The key idea for achieving this consists in integrating out exactly a certain class of high energy states, which corresponds to performing renormalization at the cubic order in the interaction strength. We test the new method on the strongly coupled two-dimensional quartic scalar theory. Our work will also be useful for the future goal of extending Hamiltonian Truncation to higher dimensions d >= 3.
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