论文标题
高斯连续张量网络的简单骨磁场理论的状态
Gaussian Continuous Tensor Network States for Simple Bosonic Field Theories
论文作者
论文摘要
张量网络允许通过各种优化找到局部晶格哈密顿量的低能状态。最近，提出了连续体中此类状态的结构，这为解决量子场理论（QFT）的目标提供了第一步。但是，连续张量网络状态（CTNS）提出的歧管很难全面研究，因为无法通过分析计算局部可观察物的期望值。在本文中，我们研究了CTNS，高斯CTNS（GCTNSS）的可拖动子类，并在简单的二次和四分之一的bosonic QFT Hamiltonians上进行基准测试。我们表明，GCTNS对二次汉密尔顿人的基态提供了任意准确的近似值，并且在弱耦合时对四分之一的估计值进行了体面的估计。由于它们捕获了我们准确考虑的理论的短距离行为，因此GCTNS甚至可以使简单差异变化恢复变化。最后，我们的研究使得CTNS确实是近似QFT的低能状态的良好多种形态是合理的。
Tensor networks states allow 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 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.
