论文标题
与哈密顿截断的相互作用量子场理论中的密度矩阵和纠缠降低
Reduced density matrix and entanglement in interacting quantum field theory with Hamiltonian truncation
论文作者
论文摘要
纠缠是古典和量子系统之间的基本差异，已成为探索高能量物理学的指导原则之一。但是，相互作用的量子场理论中纠缠熵的计算仍然具有挑战性。在这里，我们提出了使用截短的汉密尔顿方法明确计算相互作用量子场理论的减少密度矩阵的第一种方法。该方法基于整个系统的Hilbert空间与亚互相的希尔伯特空间的张量产物之间构建同构。这自然可以实现冯·诺伊曼（Von Neumann）和任意的rényi纠缠熵的计算以及相互信息，对数消极情绪和其他纠缠措施。我们的方法适用于平衡状态和实时的非平衡进化。它是独立的模型，可以应用于使用自由基础扩展的任何哈密顿截断方法。我们基于自由klein-gordon理论的方法，发现与分析结果有着极好的一致性。我们进一步证明了它在相互作用的正弦戈登模型上的潜力，研究了模型淬火后的冯·诺伊曼熵的缩放和实时动态。
Entanglement is the fundamental difference between classical and quantum systems and has become one of the guiding principles in the exploration of high- and low-energy physics. The calculation of entanglement entropies in interacting quantum field theories, however, remains challenging. Here, we present the first method for the explicit computation of reduced density matrices of interacting quantum field theories using truncated Hamiltonian methods. The method is based on constructing an isomorphism between the Hilbert space of the full system and the tensor product of Hilbert spaces of sub-intervals. This naturally enables the computation of the von Neumann and arbitrary Rényi entanglement entropies as well as mutual information, logarithmic negativity and other measures of entanglement. Our method is applicable to equilibrium states and non-equilibrium evolution in real time. It is model independent and can be applied to any Hamiltonian truncation method that uses a free basis expansion. We benchmark the method on the free Klein-Gordon theory finding excellent agreement with the analytic results. We further demonstrate its potential on the interacting sine-Gordon model, studying the scaling of von Neumann entropy in ground states and real time dynamics following quenches of the model.
