Analytic continuation works as a regularization method in physics
Analytic continuation is widely used in computational and quantum physics to extract real-frequency dynamical properties from imaginary-time simulations, and because this inverse problem is notoriously ill-posed, regularization methods are required to stabilize the solutions.
The retrieved papers consistently demonstrate that analytic continuation in physics (such as in quantum Monte Carlo or Green's function methods) is an ill-posed inverse problem that requires various regularization techniques—such as Tikhonov regularization, iterative Landweber methods, entropy penalties, and Bayesian priors—to yield stable and physically meaningful results.
Alexander Benedix Robles, Phil-Alexander Hofmann, T. Chuna, T. Dornheim, Michael Hecht. PyLIT: Reformulation and implementation of the analytic continuation problem using kernel representation methods. 2025. https://doi.org/10.1016/j.cpc.2025.109904
The paper discusses using regularization techniques such as Bayesian priors and entropic regularizers to solve the ill-conditioned analytic continuation problem in quantum many-body simulations.
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Fan Yang, Qianchao Wang, Xiaoxiao Li. A fractional Landweber iterative regularization method for stable analytic continuation. 2021. https://doi.org/10.3934/math.2021025
The study introduces a fractional Landweber iterative regularization method specifically designed to achieve stable numerical analytic continuation.
Xuemin Xue, Xiangtuan Xiong. A Posteriori Fractional Tikhonov Regularization Method for the Problem of Analytic Continuation. 2021. https://doi.org/10.3390/math9182255
The paper proposes a fractional Tikhonov regularization method to overcome the ill-posedness of the numerical analytic continuation problem in physics.
K. Ghanem, E. Koch. Connecting Tikhonov regularization to the maximum entropy method for the analytic continuation of quantum Monte Carlo data. 2022. https://doi.org/10.1103/PhysRevB.107.085129
The paper explores Tikhonov regularization under the discrepancy principle as a reliable method for the analytic continuation of quantum Monte Carlo data.
Mancheon Han, H. Choi. Parameter-free analytic continuation for quantum many-body calculations. 2022. https://doi.org/10.1103/PhysRevB.106.245150
The research develops a parameter-free analytic continuation method using kernel grids and roughness penalty regularization for quantum calculations.
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