Maximum-entropy method for analytic continuation of quantum Monte Carlo data
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (US)
An outstanding problem in the simulation of condensed-matter phenomena is how to obtain dynamical information. We consider the numerical analytic continuation of imaginary-time quantum Monte Carlo data to obtain real-frequency spectral functions. This is an extremely ill-posed problem similar to the inversion of a Laplace transform. We suggest an image-reconstruction approach, which has been widely applied to data analysis in experimental research. Specifically, we apply the maximum-entropy method (ME) to the analytic continuation of quantum Monte Carlo data. We report encouraging preliminary results for the Fano-Anderson model of an impurity state in a continuum. The incorporation of additional prior information, such as sum rules and asymptotic behavior, can be expected to significantly improve results. We compare (ME) to alternative methods. We also discuss statistical error propagation for the analytic continuation problem via the likelihood function, which is independent of the choice of image-reconstruction method. This includes the sensitivity of the data to structure in the spectral function, the optimization of Monte Carlo simulations, and how to incorporate covariance in the statistical errors of the Monte Carlo method.
- OSTI ID:
- 6939693
- Journal Information:
- Physical Review, B: Condensed Matter; (USA), Vol. 41:4; ISSN 0163-1829
- Country of Publication:
- United States
- Language:
- English
Similar Records
Dynamical properties from quantum Monte Carlo by the Maximum Entropy Method
Quantum Monte Carlo simulations and maximum entropy: Dynamics from imaginary-time data
Related Subjects
SUPERCONDUCTIVITY AND SUPERFLUIDITY
SOLIDS
ELECTRONIC STRUCTURE
ANALYTIC FUNCTIONS
ASYMPTOTIC SOLUTIONS
IMPURITIES
MONTE CARLO METHOD
NUMERICAL SOLUTION
QUANTUM MECHANICS
STATISTICAL MECHANICS
SUM RULES
VARIATIONAL METHODS
EQUATIONS
FUNCTIONS
MECHANICS
656002* - Condensed Matter Physics- General Techniques in Condensed Matter- (1987-)