论文标题
耦合激发模型中基态非分析性的纠缠谱表征
Entanglement-spectrum characterization of ground-state nonanalyticities in coupled excitation-phonon models
论文作者
论文摘要
北极星概念捕获了涉及巡回量子粒子（激发）的物理情况，该粒子与玻色子自由度强烈相互作用，并变得严重的玻色子。尽管Gerlach-löwen定理排除了与巨大层状模型的地面相关量的非分析性的发生，但在近年来，发现了与与分散无（零维）语音激发的强烈依赖性相关相互作用有关的尖锐转变的示例。在具有PEIERLS型激发与PHONON相互作用的晶格模型的示例中，此处通过激发 - Phonon系统的纠缠光谱的棱镜进行了分析。通过以数值的方式评估该频谱，可以证明，临界激发偶联强度附近的纠缠熵的行为主要源自一个特定的纠缠频谱特征值，即最小的。虽然系统的离散翻译对称性意味着这些特征值可以用裸露的Quasimomentum量子数字标记，但在这里，这些特征值可以证明它们主要与Quasimomenta $ 0 $ 0 $和$π$相关，包括两者之间在强度进行强度的情况下，包括两者之间的过渡。
The polaron concept captures physical situations involving an itinerant quantum particle (excitation) that interacts strongly with bosonic degrees of freedom and becomes heavily boson-dressed. While the Gerlach-Löwen theorem rules out the occurrence of nonanalyticities of ground-state-related quantities for a broad class of polaron models, examples were found in recent years of sharp transitions pertaining to strongly momentum-dependent interactions of an excitation with dispersionless (zero-dimensional) phonons. On the example of a lattice model with Peierls-type excitation-phonon interaction, such level-crossing-type small-polaron transitions are analyzed here through the prism of the entanglement spectrum of the excitation-phonon system. By evaluating this spectrum in a numerically-exact fashion it is demonstrated that the behavior of the entanglement entropy in the vicinity of the critical excitation-phonon coupling strength chiefly originates from one specific entanglement-spectrum eigenvalue, namely the smallest one. While the discrete translational symmetry of the system implies that those eigenvalues can be labeled by the bare-excitation quasimomentum quantum numbers, here it is shown numerically that they are predominantly associated to the quasimomenta $0$ and $π$, including cases where a transition between the two takes place deeply in the strong-coupling regime.
