用最大熵法解析延拓虚轴数据
Analytical continuation of imaginary axis data using maximum entropy
摘要：
我们研究的最大熵（MaxEnt）的方法，从虚时间到实频率的频谱数据的分析延续。总误差分为统计误差和系统误差，前者是由于输入数据中的噪声，后者是由于MaxEnt方法中使用的默认函数与精确频谱的偏差。我们发现，MaxEnt的方法在其经典的配方可能会导致两种类型的错误之间的非最佳平衡，导致不必要的大的统计误差。通过将数据分成几个批次，对每个批次执行MaxEnt计算并取平均值，可以减少统计误差。这可以超过由该方法导致的系统误差的增加。MaxEnt结果的输出可用作新MaxEnt计算的默认函数。由于统计误差的增加，这种迭代通常会导致更差的结果。通过分批分割数据，减少了统计误差，并且由于迭代导致的增加可以被系统误差的减少所超过。最后，我们考虑一个线性化的版本，以获得更好的理解的方法。
英文摘要：
We study the maximum entropy (MaxEnt) approach for analytical continuation of spectral data from imaginary times to real frequencies. The total error is divided in a statistical error, due to the noise in the input data, and a systematic error, due to deviations of the default function, used in the MaxEnt approach, from the exact spectrum. We find that the MaxEnt approach in its classical formulation can lead to a nonoptimal balance between the two types of errors, leading to an unnecessary large statistical error. The statistical error can be reduced by splitting up the data in several batches, performing a MaxEnt calculation for each batch and averaging. This can outweigh an increase in the systematic error resulting from this approach. The output from the MaxEnt result can be used as a default function for a new MaxEnt calculation. Such iterations often lead to worse results due to an increase in the statistical error. By splitting up the data in batches, the statistical error is reduced and and the increase resulting from iterations can be outweighed by a decrease in the systematic error. Finally we consider a linearized version to obtain a better understanding of the method.
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