论文标题
广义相位空间技术以探索临界量子自旋系统中的量子相变
Generalized Phase-Space Techniques to Explore Quantum Phase Transitions in Critical Quantum Spin Systems
论文作者
论文摘要
We apply the generalized Wigner function formalism to detect and characterize a range of quantum phase transitions in several cyclic, finite-length, spin-$\frac{1}{2}$ one-dimensional spin-chain models, viz., the Ising and anisotropic $XY$ models in a transverse field, and the $XXZ$ anisotropic Heisenberg model.我们利用有限的系统大小来详尽地探索每个系统的单位点，两部分和多目标相关功能。反过来，我们能够证明相位技术在见证和表征第一，第二和无限级量子相变时的实用性，同时还可以对关键系统中存在的相关性进行深入分析。我们还强调了该方法捕获旋转系统（例如地面分解和关键系统缩放）的其他特征的能力。最后，我们通过确定每个系统的状态及其构成子系统在整个量子相转换的兴趣点，使关键系统的有趣特征能够直观分析，从而证明了广义的Wigner函数的状态验证效用。
We apply the generalized Wigner function formalism to detect and characterize a range of quantum phase transitions in several cyclic, finite-length, spin-$\frac{1}{2}$ one-dimensional spin-chain models, viz., the Ising and anisotropic $XY$ models in a transverse field, and the $XXZ$ anisotropic Heisenberg model. We make use of the finite system size to provide an exhaustive exploration of each system's single-site, bipartite and multi-partite correlation functions. In turn, we are able to demonstrate the utility of phase-space techniques in witnessing and characterizing first-, second- and infinite-order quantum phase transitions, while also enabling an in-depth analysis of the correlations present within critical systems. We also highlight the method's ability to capture other features of spin systems such as ground-state factorization and critical system scaling. Finally, we demonstrate the generalized Wigner function's utility for state verification by determining the state of each system and their constituent sub-systems at points of interest across the quantum phase transitions, enabling interesting features of critical systems to be intuitively analyzed.
