热量子系统的混合净化和采样方法
Hybrid Purification and Sampling Approach for Thermal Quantum Systems
摘要：
我们提出了一种算法，结合了两种不同的方法来研究有限温度量子系统与张量网络的有益方面。一种方法是辅助方法，它给出了高精度的结果，但在低温下的尺度很差。另一种方法是最小纠缠典型热态（METTS）采样算法，该算法在低温下比辅助方法更好地扩展，并且可以并行化，但需要许多样本才能收敛到精确的结果。我们提出的这两种方法的混合净化物理站点在一个小的中心空间区域与合作伙伴的附属网站，其余的网站使用METTS算法进行采样。在纯化的集群内测量的观测值具有比METTS方法低得多的样本方差，而对集群外的站点进行采样减少了它们的纠缠和算法的计算成本。该算法的采样步骤保持直接并行化。混合方法还解决了METTS的一个重要技术问题，该问题使得难以从量子数守恒中受益。通过研究S=1的海森堡阶梯系统，我们发现混合算法在中等温度和高纠缠度的系统中比辅助算法和METTS算法收敛得更快。
英文摘要：
We propose an algorithm which combines the beneficial aspects of two different methods for studying finite-temperature quantum systems with tensor networks. One approach is the ancilla method, which gives high-precision results but scales poorly at low temperatures. The other method is the minimally entangled typical thermal state (METTS) sampling algorithm which scales better than the ancilla method at low temperatures and can be parallelized, but requires many samples to converge to a precise result. Our proposed hybrid of these two methods purifies physical sites in a small central spatial region with partner ancilla sites, sampling the remaining sites using the METTS algorithm. Observables measured within the purified cluster have much lower sample variance than in the METTS approach, while sampling the sites outside the cluster reduces their entanglement and the computational cost of the algorithm. The sampling steps of the algorithm remain straightforwardly parallelizable. The hybrid approach also solves an important technical issue with METTS that makes it difficult to benefit from quantum number conservation. By studying S=1 Heisenberg ladder systems, we find the hybrid method converges more quickly than both the ancilla and METTS algorithms at intermediate temperatures and for systems with higher entanglement.
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