We present an unconstrained tree tensor network approach to the study of lattice gauge theories in two spatial dimensions showing how to perform numerical simulations of theories in presence of fermionic matter and four-body magnetic terms, at zero and finite density, with periodic and open boundary conditions. We exploit the quantum link representation of the gauge fields and demonstrate that a fermionic rishon representation of the quantum links allows us to efficiently handle the fermionic matter while finite densities are naturally enclosed in the tensor network description. We explicit perform calculations for quantum electrodynamics in the spin-one quantum link representation on lattice sizes of up to 16x16 sites, detecting and characterizing different quantum regimes. In particular, at finite density, we detect signatures of a phase separation as a function of the bare mass values at different filling densities. The presented approach can be extended straightforwardly to three spatial dimensions.

中文翻译：

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有限密度的二维量子链晶格量子电动力学

我们提出了一种不受约束的树张量网络方法，用于二维空间晶格规范理论的研究，显示了如何在存在费米离子物质和四体磁项的情况下，在零密度和有限密度下，以周期性和开放边界进行理论模拟条件。我们利用了规范场的量子链接表示，并证明了量子链接的费米离子rishon表示使我们能够有效地处理费米离子物质，而有限密度自然包含在张量网络描述中。我们在自旋一量子链接表示中对多达16x16的晶格大小进行显式的量子电动力学计算，以检测和表征不同的量子态。特别是在有限的密度下 我们在不同的填充密度下检测到相分离的特征与裸质量值的函数。所提出的方法可以直接扩展到三个空间维度。