We report on the calculation of the symmetry resolved entanglement entropies in two-dimensional many-body systems of free bosons and fermions by \emph{dimensional reduction}. When the subsystem is translational invariant in a transverse direction, this strategy allows us to reduce the initial two-dimensional problem into decoupled one-dimensional ones in a mixed space-momentum representation. While the idea straightforwardly applies to any dimension $d$, here we focus on the case $d=2$ and derive explicit expressions for two lattice models possessing a $U(1)$ symmetry, i.e., free non-relativistic massless fermions and free complex (massive and massless) bosons. Although our focus is on symmetry resolved entropies, some results for the total entanglement are also new. Our derivation gives a transparent understanding of the well known different behaviours between massless bosons and fermions in $d\geq2$: massless fermions presents logarithmic violation of the area which instead strictly hold for bosons, even massless. This is true both for the total and the symmetry resolved entropies. Interestingly, we find that the equipartition of entanglement into different symmetry sectors holds also in two dimensions at leading order in subsystem size; we identify for both systems the first term breaking it. All our findings are quantitatively tested against exact numerical calculations in lattice models for both bosons and fermions.

中文翻译：

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对称性通过降维解决二维系统中的纠缠

我们报告了通过 \emph {降维} 计算自由玻色子和费米子的二维多体系统中的对称解决纠缠熵。当子系统在横向上具有平移不变性时，该策略允许我们在混合空间-动量表示中将初始二维问题简化为解耦的一维问题。虽然这个想法直接适用于任何维度 $d$，但这里我们专注于 $d=2$ 的情况并推导出具有 $U(1)$ 对称性的两个晶格模型的显式表达式，即自由非相对论无质量费米子和自由复合（有质量和无质量）玻色子。尽管我们的重点是对称解析熵，但总纠缠的一些结果也是新的。我们的推导对 $d\geq2$ 中无质量玻色子和费米子之间众所周知的不同行为给出了一个透明的理解：无质量费米子呈现区域的对数违反，而对玻色子严格保持，甚至无质量。这对于总熵和对称分辨熵都是正确的。有趣的是，我们发现纠缠到不同对称扇区的均分在子系统大小的领先顺序中也适用于二维；我们为这两个系统确定了打破它的第一个术语。我们所有的发现都针对玻色子和费米子的晶格模型中的精确数值计算进行了定量测试。这对于总熵和对称分辨熵都是正确的。有趣的是，我们发现纠缠到不同对称扇区的均分在子系统大小的领先顺序中也适用于二维；我们为这两个系统确定了打破它的第一个术语。我们所有的发现都针对玻色子和费米子的晶格模型中的精确数值计算进行了定量测试。这对于总熵和对称分辨熵都是正确的。有趣的是，我们发现纠缠到不同对称扇区的均分在子系统大小的领先顺序中也适用于二维；我们为这两个系统确定了打破它的第一个术语。我们所有的发现都针对玻色子和费米子的晶格模型中的精确数值计算进行了定量测试。