U(1)对称量子自旋模型中有效转子/自旋波分离的纠缠动力学
Entangling dynamics from effective rotor/spin-wave separation in U(1)-symmetric quantum spin models
AI总结：
本研究揭示U(1)对称自旋模型中零动量与有限动量自由度分离机制，使幂律相互作用系统复现OAT模型动力学，定量解释自旋压缩与猫态生成，并推广至更广模型类别。
摘要：
量子自旋模型的非平衡动力学是一个极具挑战性的课题，这源于希尔伯特空间的指数复杂性；同时，它对于理解最先进的量子模拟器能够生成的多体纠缠态至关重要。一类特别重要的演化由U(1)对称哈密顿量控制，其初始态破坏了U(1)对称性——典型的例子是所谓的单轴扭转（OAT）模型的演化，该模型具有自旋之间的无限范围相互作用。在这项工作中，我们展示了OAT模型的动力学可以通过具有幂律衰减相互作用的系统来紧密复现，这得益于零动量自由度（与所谓的安德森塔态相关）与有限动量自由度（与自旋波激发相关）之间的有效分离，前者重构了OAT模型。这一机制定量解释了最近在偶极哈密顿量动力学中观察到的自旋压缩和薛定谔猫态生成的数值结果；并且它为将这一观察扩展到对量子模拟具有直接意义的更广泛模型类别铺平了道路。
英文摘要：
The non-equilibrium dynamics of quantum spin models is a most challenging topic, due to the exponentiality of Hilbert space; and it is central to the understanding of the many-body entangled states that can be generated by state-of-the-art quantum simulators. A particularly important class of evolutions is the one governed by U(1) symmetric Hamiltonians, initialized in a state which breaks the U(1) symmetry -- the paradigmatic example being the evolution of the so-called one-axis-twisting (OAT) model, featuring infinite-range interactions between spins. In this work we show that the dynamics of the OAT model can be closely reproduced by systems with power-law-decaying interactions, thanks to an effective separation between the zero-momentum degrees of freedom, associated with the so-called Anderson tower of states, and reconstructing a OAT model; and finite-momentum ones, associated with spin-wave excitations. This mechanism explains quantitatively the recent numerical observation of spin squeezing and Schrödinger-cat generation in the dynamics of dipolar Hamiltonians; and it paves the way for the extension of this observation to a much larger class of models of immediate relevance for quantum simulations.
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