We present a new tensor network algorithm for calculating the partition function of interacting quantum field theories in 2 dimensions. It is based on the Tensor Renormalization Group (TRG) protocol, adapted to operate entirely at the level of fields. This strategy was applied in Ref.[1] to the much simpler case of a free boson, obtaining an excellent performance. Here we include an arbitrary self-interaction and treat it in the context of perturbation theory. A real space analogue of the Wilsonian effective action and its expansion in Feynman graphs is proposed. Using a $\lambda \phi^4$ theory for benchmark, we evaluate the order $\lambda$ correction to the free energy. The results show a fast convergence with the bond dimension, implying that our algorithm captures well the effect of interaction on entanglement.

中文翻译：

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相互作用量子场的张量重整化群

我们提出了一种新的张量网络算法，用于计算二维相互作用量子场论的配分函数。它基于张量重整化组 (TRG) 协议，适用于完全在字段级别操作。参考文献[1]中应用了该策略 到自由玻色子的更简单的情况，获得出色的性能。在这里，我们包含了一个任意的自相互作用，并在扰动理论的背景下对其进行了处理。提出了威尔逊有效作用的真实空间模拟及其在费曼图中的扩展。使用 $\lambda \phi^4$ 理论作为基准，我们评估了对自由能的 $\lambda$ 校正顺序。结果显示了与键维数的快速收敛，这意味着我们的算法很好地捕捉了相互作用对纠缠的影响。