Tensor networks states allow one to find the low-energy states of local lattice Hamiltonians through variational optimization. Recently, a construction of such states in the continuum was put forward, providing a first step towards the goal of solving quantum field theories (QFTs) variationally. However, the proposed manifold of continuous tensor network states (CTNSs) is difficult to study in full generality, because the expectation values of local observables cannot be computed analytically. In this paper we study a tractable subclass of CTNSs, the Gaussian CTNSs (GCTNSs), and benchmark them on simple quadratic and quartic bosonic QFT Hamiltonians. We show that GCTNSs provide arbitrarily accurate approximations to the ground states of quadratic Hamiltonians and decent estimates for quartic ones at weak coupling. Since they capture the short distance behavior of the theories we consider exactly, GCTNSs even allow one to renormalize away simple divergences variationally. In the end our study makes it plausible that CTNSs are indeed a good manifold to approximate the low-energy states of QFTs.

中文翻译：

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简单玻色场理论的高斯连续张量网络状态

张量网络状态允许人们通过变分优化找到局部晶格哈密顿量的低能状态。最近，提出了在连续体中构造这种状态的方法，为朝着可变地解决量子场论（QFT）的目标迈出了第一步。然而，由于无法通过分析计算局部可观测值的期望值，因此难以全面地研究所提出的连续张量网络状态（CTNS）的流形。在本文中，我们研究了CTNS的易处理子类，即高斯CTNS（GCTNS），并以简单的二次和四次玻色子QFT哈密顿量为基准。我们表明，GCTNSs为二次哈密顿量的基态提供了任意准确的近似值，并为弱耦合时的四次哈密顿量提供了体面的估计。由于它们捕获了我们精确考虑的理论的短距离行为，因此GCTNS甚至允许人们以变分形式对简单散度重新进行归一化。最后，我们的研究使CTNS确实是近似QFT低能态的良好流形。