Hamiltonian Truncation有效理论中的高阶结构
Higher-order structure of Hamiltonian truncation effective theory
AI总结：
本文提出了一种基于Hamiltonian截断有效理论的方法，通过系统性地包含修正项来减轻截断伪影，并发展了两种互补的扩展，以更准确地描述高阶结构。
摘要：
我们研究了在Hamiltonian truncation有效理论框架下，二维λϕ^4理论的Hamiltonian截断，其中通过系统性地包含按逆紫外能截断E_max的幂次组织的修正项来减轻截断伪影。在主导阶匹配程序的基础上，我们开发了两种互补的扩展。首先，我们推导出局部匹配修正的紧凑所有阶表达式，通过重新求和具有固定拓扑的无限类图来得到质量和四次耦合的修正。其次，我们通过连续体优先匹配程序扩展了非局部部分，计算贡献于O(E_max^{-4})的次次非局部修正，其中有效修正在无限体积中计算，随后将空间方向重新紧凑化，以获得一个分离的希尔伯特空间基，用于实施截断算符构造。我们的结果表明，为了在主导阶之外描述理论，需要越来越丰富的算符基。
英文摘要：
We study the Hamiltonian truncation for the two-dimensional $λϕ^4$ theory within the framework of Hamiltonian truncation effective theory, where truncation artifacts are mitigated through a systematic inclusion of corrective terms organized in inverse powers of the ultraviolet energy cut-off $E_{\rm max}$. Building on the leading-order matching program, we develop two complementary extensions. First, we derive compact all-order expressions for the local matching corrections to the mass and quartic coupling by resumming infinite classes of diagrams sharing fixed topologies within the local approximation. Second, we extend the non-local sector by computing the next-to-next-to-local corrections contributing at $\mathcal{O}(E_{\rm max}^{-4})$, following a continuum-first matching procedure, in which the effective corrections are computed in infinite volume and the spatial direction is subsequently re-compactified to obtain a discrete basis of free-Hamiltonian eigenstates on which the truncated operator construction is implemented. Our results show that an increasingly rich operator basis is necessary to describe the theory beyond leading order.
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