Sachdev-Ye-Kitaev模型中的单体观测量
Single-Instance Observables in the Sachdev-Ye-Kitaev Model
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中文总结 AI 辅助
本文提出SYK模型中低权重马约拉纳弦热期望值的图解展开，按N^{-1/2}幂次组织，可高效计算，并应用于MQ模型以提升热场双态保真度。
中文摘要 AI 辅助
我们针对$N$费米子Sachdev--Ye--Kitaev（SYK）模型的固定实现，提出了低权重马约拉纳弦热期望值的图解展开方法。在展开的每一阶，观测量表示为耦合常数多项式的有限和，乘以由大$N$melon传播子构建的依赖于温度的核函数。在固定的$\eta J$下，展开按$N^{-1/2}$的幂次组织，每一阶都可以用$N$的多项式规模的经典资源高效计算。该展开还适用于任意虚时以及足够短实时的关联函数。对于四体SYK模型，我们展示了图解预测在$N$最大为24的尺寸下与精确对角化结果高度吻合。我们还将该方法应用于由两个相同固定SYK实现副本构成的Maldacena--Qi（MQ）模型。这使我们能够识别出一个近似的SYK型哈密顿量，其热场双态与Maldacena--Qi基态的保真度高于原始SYK哈密顿量的热场双态。
英文摘要
We present a diagrammatic expansion for thermal expectation values of low-weight Majorana strings in a fixed realization of the $N$-fermion Sachdev--Ye--Kitaev (SYK) model. At each order in the expansion, the observable is expressed as a finite sum of polynomials in the couplings multiplied by temperature-dependent kernels built from the large-$N$ melonic propagator. At fixed $βJ$, the expansion is organized in powers of $N^{-1/2}$, and each order can be efficiently evaluated with classical resources polynomial in $N$. The expansion also extends to correlations at arbitrary imaginary times and sufficiently short real times. For the four-body SYK model, we show that the diagrammatic predictions give an excellent account of exact diagonalization results at sizes up to $N=24$. We also apply the method to the Maldacena--Qi (MQ) model formed from two identical copies of a fixed SYK realization. This enables the identification of a nearby SYK-like Hamiltonian whose thermofield double state has higher fidelity with the Maldacena--Qi ground state than the thermofield double of the original SYK Hamiltonian.
发表机构
- Brandeis University（布兰迪斯大学）
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