In this work we calculate the entanglement entropy of certain excited states of the quantum Lifshitz model. The quantum Lifshitz model is a 2 + 1-dimensional bosonic quantum field theory with an anisotropic scaling symmetry between space and time that belongs to the universality class of the quantum dimer model and its generalizations. The states we consider are constructed by exciting the eigenmodes of the Laplace-Beltrami operator on the spatial manifold of the model. We perform a replica calculation and find that, whenever a simple assumption is satisfied, the bipartite entanglement entropy of any such excited state can be evaluated analytically. We show that the assumption is satisfied for all excited states on the rectangle and for almost all excited states on the sphere and provide explicit examples in both geometries. We find that the excited state entanglement entropy obeys an area law and is related to the entanglement entropy of the ground state by two universal constants. We observe a logarithmic dependence on the excitation number when all excitations are put onto the same eigenmode.

中文翻译：

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量子 Lifshitz 模型中激发态的纠缠熵

在这项工作中，我们计算了量子 Lifshitz 模型的某些激发态的纠缠熵。量子 Lifshitz 模型是 2 + 1 维玻色子量子场论，在空间和时间之间具有各向异性标度对称，属于量子二聚体模型及其推广的普适性类。我们考虑的状态是通过在模型的空间流形上激发 Laplace-Beltrami 算子的本征模来构造的。我们执行副本计算并发现，只要满足一个简单的假设，就可以分析评估任何此类激发态的二分纠缠熵。我们表明对于矩形上的所有激发态和球体上的几乎所有激发态都满足该假设，并在两种几何结构中提供了明确的示例。我们发现激发态纠缠熵遵循面积定律，并且通过两个通用常数与基态的纠缠熵相关。当所有激发都放在相同的本征模式上时，我们观察到对激发数的对数依赖性。