Related papers: Connecting Tikhonov regularization to the maximum …
A new algorithm for analytic continuation of noisy quantum Monte Carlo (QMC) data from the Matsubara domain to real frequencies is proposed. Unlike the widely used maximum-entropy (MaxEnt) procedure, our method is linear with respect to…
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…
This study explores the use of neural network-based analytic continuation to extract spectra from Monte Carlo data. We apply this technique to both synthetic and Monte Carlo-generated data. The training sets for neural networks are…
Many fields of physics use quantum Monte Carlo techniques, but struggle to estimate dynamic spectra via the analytic continuation of imaginary-time quantum Monte Carlo data. One of the most ubiquitous approaches to analytic continuation is…
Quantum Monte Carlo (QMC) methods are uniquely capable of providing exact simulations of quantum many-body systems. Unfortunately, the applications of a QMC simulation are limited because extracting dynamic properties requires solving the…
We report multipronged progress on the stochastic averaging approach to numerical analytic continuation of quantum Monte Carlo data. With the sampled spectrum parametrized with delta-functions in continuous frequency space, a calculation of…
Inferring a quantum system from incomplete information is a common problem in many aspects of quantum information science and applications, where the principle of maximum entropy (MaxEnt) plays an important role. The quantum state…
We present an algorithm for the analytic continuation of imaginary-time quantum Monte Carlo data which is strictly based on principles of Bayesian statistical inference. Within this framework we are able to obtain an explicit expression for…
Maximum entropy method for analytic continuation is extended by introducing quantum relative entropy. This new method is formulated in terms of matrix-valued functions and therefore invariant under arbitrary unitary transformation of input…
We develop a novel analytic continuation method for self-energies on the Matsubara domain as computed by quantum Monte Carlo simulations within dynamical mean field theory (QMC+DMFT). Unlike a maximum entropy (maxEn) procedure employed for…
We exploit the similarities between Tikhonov regularization and Bayesian hierarchical models to propose a regularization scheme that acts like a distributed Tikhonov regularization where the amount of regularization varies from component to…
We present $\texttt{Maxent}$, a tool for performing analytic continuation of spectral functions using the maximum entropy method. The code operates on discrete imaginary axis datasets (values with uncertainties) and transforms this input to…
We study multi-parameter regularization (multiple penalties) for solving linear inverse problems to promote simultaneously distinct features of the sought-for objects. We revisit a balancing principle for choosing regularization parameters…
We study multi-parameter Tikhonov regularization, i.e., with multiple penalties. Such models are useful when the sought-for solution exhibits several distinct features simultaneously. Two choice rules, i.e., discrepancy principle and…
A simple method for numerical analytic continuation is developed. It is designed to analytically continue the imaginary time (Matsubara frequency) quantum Monte Carlo simulation results to the real time (real frequency) domain. Such a…
The maximum entropy method is shown to be a special limit of the stochastic analytic continuation method introduced by Sandvik [Phys. Rev. B 57, 10287 (1998)]. We employ a mapping between the analytic continuation problem and a system of…
In the paper, we study the convergence analysis of Tikhonov regularization in finding a zero of a maximal monotone operator using the notion of R-continuity. Applications to convex minimization and DC programming are provided.
In this work, we consider ill-posed inverse problems in which the forward operator is continuous and weakly closed, and the sought solution belongs to a weakly closed constraint set. We propose a regularization method based on minimizing…
We study the behaviour of Tikhonov regularisation on topological spaces with multiple regularisation terms. The main result of the paper shows that multi-parameter regularisation is well-posed in the sense that the results depend…
Analytic continuation of numerical data obtained in imaginary time or frequency has become an essential part of many branches of quantum computational physics. It is, however, an ill-conditioned procedure and thus a hard numerical problem.…