用小波表示研究量子场论中的纠缠
Entanglement in quantum field theory via wavelet representations
摘要：
量子场论（QFT）使用连续场描述自然，但QFT的物理性质通常是在有限分辨率下通过测量可观测量来揭示的。我们描述了一个多尺度表示的自由标量玻色子和伊辛模型费米子QFT小波。利用小波基函数的正交性和自相似性，我们证明了一些著名的关系，如尺度相关的子系统纠缠熵和重正化的关联在基态。我们还发现了一些新的应用小波变换作为压缩表示的基态的QFT，可以用来说明量子相变通过保真度重叠和全息纠缠的纯化。
英文摘要：
Quantum field theory (QFT) describes nature using continuous fields, but physical properties of QFT are usually revealed in terms of measurements of observables at a finite resolution. We describe a multiscale representation of a free scalar bosonic and Ising model fermionic QFTs using wavelets. Making use of the orthogonality and self similarity of the wavelet basis functions, we demonstrate some well known relations such as scale dependent subsystem entanglement entropy and renormalization of correlations in the ground state. We also find some new applications of the wavelet transform as a compressed representation of ground states of QFTs which can be used to illustrate quantum phase transitions via fidelity overlap and holographic entanglement of purification.
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