用于量子模拟的全量规固定 SU(2) 哈密顿方程

Dorota M. Grabowska, Christopher F. Kane, Christian W. Bauer
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引用次数: 0

摘要

我们展示了如何为纯粹的 SU(2) 轨则理论构建一个完全轨则固定的晶格哈密顿。我们的工作是在先前工作的基础上发展而来的,在先前的工作中,我们提出了一种在所有轨距耦合值下都能有效模拟的 SU(2) 格规理论。这一表述利用了最大树规度,即所有局部规度对称性都被固定,而残余的全局规度对称性依然存在。通过把苏(2)晶格规理论的几何图象看作一个旋转棒系统,我们演示了如何固定剩余的全局规对称性。特别是,通过使用三个欧拉角在实验室和体框架之间旋转,可以分离出与总电荷相关的量子数。在这种新的 "后置 "基础上,希尔伯特空间被清晰地划分为具有不同总角动量的扇区,这使得对特定总电荷扇区的量规固定变得非常简单,尤其是对于零电荷扇区。除了这个sequestered basis 继承了在所有耦合值下都有效的特性之外,我们还证明,尽管最终的规整过程是全局性的,但这个哈密顿可以用量子资源来模拟,而量子资源只与晶格体积成多项式缩放。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A Fully Gauge-Fixed SU(2) Hamiltonian for Quantum Simulations
We demonstrate how to construct a fully gauge-fixed lattice Hamiltonian for a pure SU(2) gauge theory. Our work extends upon previous work, where a formulation of an SU(2) lattice gauge theory was developed that is efficient to simulate at all values of the gauge coupling. That formulation utilized maximal-tree gauge, where all local gauge symmetries are fixed and a residual global gauge symmetry remains. By using the geometric picture of an SU(2) lattice gauge theory as a system of rotating rods, we demonstrate how to fix the remaining global gauge symmetry. In particular, the quantum numbers associated with total charge can be isolated by rotating between the lab and body frames using the three Euler angles. The Hilbert space in this new `sequestered' basis partitions cleanly into sectors with differing total angular momentum, which makes gauge-fixing to a particular total charge sector trivial, particularly for the charge-zero sector. In addition to this sequestered basis inheriting the property of being efficient at all values of the coupling, we show that, despite the global nature of the final gauge-fixing procedure, this Hamiltonian can be simulated using quantum resources scaling only polynomially with the lattice volume.
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