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 the 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 explicitly perform calculations for quantum electrodynamics in the spin-one quantum-link representation on lattice sizes of up to $16\times 16$ 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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有限密度下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来研究二维空间中的晶格规范理论，展示了如何在存在费米离子物质和四体磁项（零密度和有限密度）的情况下对理论进行数值模拟，其中周期性和开放性边界条件。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勒里森表示使我们能够有效地处理费米子物质，而有限密度自然包含在张量网络描述中。我们明确地对自旋一量子链表示中的量子电动力学进行计算，其晶格尺寸最大为$16\times 16$位置，检测和表征不同的量子态。特别是在有限的密度下，我们检测到在不同的填充密度下，相分离的特征与裸质量值的函数关系。所提出的方法可以直接扩展到三个空间维度。