Sandvik Anders W
Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA and Institute of Physics, Chinese Academy of Sciences, P.O. Box 603, Beijing 100190, China.
Phys Rev E. 2016 Dec;94(6-1):063308. doi: 10.1103/PhysRevE.94.063308. Epub 2016 Dec 27.
A method for analytic continuation of imaginary-time correlation functions (here obtained in quantum Monte Carlo simulations) to real-frequency spectral functions is proposed. Stochastically sampling a spectrum parametrized by a large number of δ functions, treated as a statistical-mechanics problem, it avoids distortions caused by (as demonstrated here) configurational entropy in previous sampling methods. The key development is the suppression of entropy by constraining the spectral weight to within identifiable optimal bounds and imposing a set number of peaks. As a test case, the dynamic structure factor of the S=1/2 Heisenberg chain is computed. Very good agreement is found with Bethe ansatz results in the ground state (including a sharp edge) and with exact diagonalization of small systems at elevated temperatures.
提出了一种将虚时关联函数（此处通过量子蒙特卡罗模拟获得）解析延拓为实频谱函数的方法。通过将由大量δ函数参数化的谱进行随机采样，将其视为一个统计力学问题，该方法避免了（如本文所示）先前采样方法中由构型熵引起的失真。关键进展在于通过将谱权重限制在可识别的最佳界限内并施加固定数量的峰来抑制熵。作为一个测试案例，计算了S = 1/2海森堡链的动态结构因子。结果发现，在基态下与贝塞耳假设结果（包括尖锐边缘）以及在高温下与小系统的精确对角化结果都有很好的一致性。
