论文标题
Sachdev-ye-Kitaev模型的变分波函数
Variational wavefunctions for Sachdev-Ye-Kitaev models
论文作者
论文摘要
考虑到一类$ q $ - 本地的哈密顿量，是否可以找到一个简单的变化状态，其能量是热力学极限中基态能量的有限级分？尽管产品状态在玻色粒（或Qubit）模型的情况下通常会提供肯定的答案，但我们表明高斯州在费米子情况下急剧失败，例如Sachdev-ye-Kitaev（Syk）模型。这促使我们为受变量耦合群集算法启发的SYK模型提出了一类新的波形函数。我们介绍了一个静态（“ 0+0d”）大$ n $场理论，以研究这些状态的能量，两点相关器和纠缠属性。最重要的是，我们证明了$ r \ $ r \ $ r \ $ r \ $ r \ y之间的有限疾病平均近似值约为0.62 $，以$ q = 4 $，syk的变异状态和基态能量。此外，各变化态提供了相关的两种风味SYK模型中自发对称性破裂的精确描述。
Given a class of $q$-local Hamiltonians, is it possible to find a simple variational state whose energy is a finite fraction of the ground state energy in the thermodynamic limit? Whereas product states often provide an affirmative answer in the case of bosonic (or qubit) models, we show that Gaussian states fail dramatically in the fermionic case, like for the Sachdev-Ye-Kitaev (SYK) models. This prompts us to propose a new class of wavefunctions for SYK models inspired by the variational coupled cluster algorithm. We introduce a static ("0+0D") large-$N$ field theory to study the energy, two-point correlators, and entanglement properties of these states. Most importantly, we demonstrate a finite disorder-averaged approximation ratio of $r \approx 0.62$ between the variational and ground state energy of SYK for $q=4$. Moreover, the variational states provide an exact description of spontaneous symmetry breaking in a related two-flavor SYK model.
