论文标题
完全连接的量子碱模型中的平衡和动态相变：近似能量本征和关键时间
Equilibrium and dynamical phase transitions in fully connected quantum Ising model: Approximate energy eigenstates and critical time
论文作者
论文摘要
我们研究有限大小完全连接的ISING模型的平衡以及在零温度下具有横向场的动力学特性。关于平衡，我们提出了具有较大重叠的近似地面和第一激发状态（除相换点附近）具有确切的能量本质。对于近似和精确的本征态，我们计算量子纠缠的能量差距，一致和几何度量。在能量差距和近似本征态之间的几何纠缠的情况下，我们观察到了良好的匹配。鉴于，当系统大小较大时，同意仅在顺磁性阶段显示出一个不错的一致性。在淬灭动力学中，我们研究了基于动态顺序参数和loschmidt速率，在动态相变中起重要作用的时间段和第一个关键时间。当所有旋转最初都在它们相互作用的方向上极化时，时间段和关键时间都与动力学临界点处的系统大小对数分化。当所有旋转最初都朝横向场的方向发展时，时间段和关键时间都会表现出对数或幂律分歧，具体取决于最终场强。在收敛的情况下，我们提供了有限尺寸缩放和融合值的估计值。
We study equilibrium as well as dynamical properties of the finite-size fully connected Ising model with a transverse field at the zero temperature. In relation to the equilibrium, we present approximate ground and first excited states that have large overlap -- except near the phase transition point -- with the exact energy eigenstates. For both the approximate and exact eigenstates, we compute the energy gap, concurrence, and geometric measure of quantum entanglement. We observe a good match in the case of energy gap and geometric entanglement between the approximate and exact eigenstates. Whereas, when the system size is large, the concurrence shows a nice agreement only in the paramagnetic phase. In a quench dynamics, we study the time period and the first critical time, which play important roles in the dynamical phase transitions, based on a dynamical order parameter and the Loschmidt rate, respectively. When all the spins are initially polarized in the direction of their mutual interaction, both the time period and critical time diverges logarithmically with the system size at the dynamical critical point. When all the spins are initially in the direction of transverse field, both the time period and critical time exhibit logarithmic or power-law divergences depending on the final field strength. In the case of convergence, we provide estimates for the finite-size scaling and converged value.
