从头算全息术
Ab initio holography
摘要：
利用量子重整化群构造了格点上复玻色子U（N）矢量模型的全息对偶。当决定空间连通性的跳跃振幅被提升为量子变量时，体几何变得动态。在大N极限下，数值求解了有限系统动力学跳跃场的全体积运动方程。从有限尺寸标度，我们表明，不同的阶段表现出不同的几何特征的散装。在绝缘阶段，空间被分割成孤立的岛屿深入体内，表现出超局域性。在超流相中，体块呈现出一个视界，超过该视界，几何形状就变得非局部。就在视界处，跳跃场在坐标距离上以普适的幂律衰减，而在视界内则以指数连续变化的较慢的幂律衰减。在临界点，散装表现出局部几何特征的长度尺度渐近发散的IR限制。
英文摘要：
We apply the quantum renormalization group to construct a holographic dual for the U(N) vector model for complex bosons defined on a lattice. The bulk geometry becomes dynamical as the hopping amplitudes which determine connectivity of space are promoted to quantum variables. In the large N limit, the full bulk equations of motion for the dynamical hopping fields are numerically solved for finite systems. From finite size scaling, we show that different phases exhibit distinct geometric features in the bulk. In the insulating phase, the space gets fragmented into isolated islands deep inside the bulk, exhibiting ultra-locality. In the superfluid phase, the bulk exhibits a horizon beyond which the geometry becomes non-local. Right at the horizon, the hopping fields decay with a universal power-law in coordinate distance between sites, while they decay in slower power-laws with continuously varying exponents inside the horizon. At the critical point, the bulk exhibits a local geometry whose characteristic length scale diverges asymptotically in the IR limit.
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