近日，德国柏林自由大学的S. J. Thomson与J. Eisert合作并取得一项新进展。经过不懈努力，他们利用流动方程解开量子动力学。相关研究成果已于2024年7月2日在国际知名学术期刊《自然—物理学》上发表。

在这项工作中，研究人员提出了一种能够复杂性理论障碍的技术，通过将连续酉流技术与新开发的置乱变换方法相结合。研究人员克服了这样的假设，即近似对角化哈密顿量不能导致相对较长时间的可靠预测。相反，研究人员表明该方法在局部和非局部阶段都达到了良好的精度，并对包括无限温度自相关函数在内的许多量进行了可靠的预测。他们用截断误差的严格增量界限来补充该发现。

该研究方法表明，在实践中，对中等尺度时间演化的探索可能比通常假设的更可行，这对近期量子模拟器提出了挑战。

据悉，强关联系统中多体量子动力学的研究极具挑战性。迄今为止，能够模拟二维量子系统非平衡动力学的数值方法很少，这在一定程度上是由于复杂性理论的障碍。

附：英文原文

Title: Unravelling quantum dynamics using flow equations

Author: Thomson, S. J., Eisert, J.

Issue&Volume: 2024-07-02

Abstract: The study of many-body quantum dynamics in strongly correlated systems is extremely challenging. To date, few numerical methods exist that are capable of simulating the non-equilibrium dynamics of two-dimensional quantum systems, which is partly due to complexity theoretic obstructions. In this work, we present a technique able to overcome this obstacle, by combining continuous unitary flow techniques with the newly developed method of scrambling transforms. We overcome the assumption that approximately diagonalizing the Hamiltonian cannot lead to reliable predictions for relatively long times. Rather, we show that the method achieves good accuracy in both localized and delocalized phases and makes reliable predictions for a number of quantities including infinite-temperature autocorrelation functions. We complement our findings with rigorous incremental bounds on the truncation error. Our approach shows that, in practice, the exploration of intermediate-scale time evolution may be more feasible than is commonly assumed, challenging near-term quantum simulators.

DOI: 10.1038/s41567-024-02549-2

Source: https://www.nature.com/articles/s41567-024-02549-2