用于有限温度计算的改进 Hilbert 空间探索算法
Improved Hilbert space exploration algorithms for finite temperature calculations
AI总结：
本文针对 Lieb-Liniger 模型开发了一种新的 Hilbert 空间探索算法，专门优化有限熵态下密度相关算符关联函数的计算顺序，改进了 ABACUS 库在高熵态（如有限温度或量子淬火后）计算中的不足。
摘要：
计算强相互作用量子系统中的关联函数是现代凝聚态理论中最重要的挑战之一，因为它们在描述许多物理可观测量时非常重要。同时，由于传统的微扰方法不适用或数值方法的少体限制，这一挑战也是最难解决的问题之一。对于模型可积的特殊情况，基于 Bethe Ansatz 的方法已成功计算出能谱，并为我们提供了物理上重要算符矩阵元的解析表达式。然而，利用这些结果来计算关联函数通常需要对本征态上的求和进行数值计算。为了高效地执行这些求和，人们开发了 Hilbert 空间探索算法，其中最著名的是 ABACUS 库。虽然该库在计算基态或低熵态的关联时表现良好，但对于高熵态（最重要的是在有限温度下或量子淬火后）的情况则更为困难，仍有改进空间。在本工作中，我们为 Lieb-Liniger 模型开发了一种新的 Hilbert 空间探索算法，专门针对密度相关算符的关联来优化有限熵态上的计算顺序。
英文摘要：
Computing correlation functions in strongly-interacting quantum systems is one of the most important challenges of modern condensed matter theory, due to their importance in the description of many physical observables. Simultaneously, this challenge is one of the most difficult to address, due to the inapplicability of traditional perturbative methods or the few-body limitations of numerical approaches. For special cases, where the model is integrable, methods based on the Bethe Ansatz have succeeded in computing the spectrum and given us analytical expressions for the matrix elements of physically important operators. However, leveraging these results to compute correlation functions generally requires the numerical evaluation of summations over eigenstates. To perform these summations efficiently, Hilbert space exploration algorithms have been developed which has resulted most notably in the ABACUS library. While this performs quite well for correlations on ground states or low-entropy states, the case of high entropy states (most importantly at finite temperatures or after a quantum quench) is more difficult, and leaves room for improvement. In this work, we develop a new Hilbert space exploration algorithm for the Lieb-Liniger model, specially tailored to optimize the computational order on finite-entropy states for correlations of density-related operators.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
