Abstract
Computer simulations of many-body systems can present difficult data analysis problems. An example is the determination of dynamical properties from quantum Monte Carlo (QMC) simulations. Data on imaginary time Matsubara Greens’ functions implicitly contain information about real time behavior. However, the spectral representation which relates imaginary time to real time is similar to a Laplace transform, and the numerical inversion of such transforms is notoriously unstable in the presence of statistical noise. Another example is the determination of the densities of states and the thermodynamic functions from imprecise knowledge of a finite number of moments. Data analysis problems in computer simulations are similar in many respects to those found in experimental research. They are often inverse problems, they can be ill-posed, the data may be incomplete, and they may be subject to statistical and systematic errors. Fortunately, the recent conceptual and algorithmic advances in maximum entropy (Max-Ent) and Bayesian data analysis methods1 are equally applicable to computer simulations. We illustrate such applications by calculating the dynamical properties of the Anderson model for dilute magnetic alloys and the densities of states of the 2-D Heisenberg model.
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© 1992 Springer Science+Business Media New York
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Silver, R.N., Gubernatis, J.E., Sivia, D.S., Jarrell, M., Roeder, H. (1992). Applications of Maximum Entropy and Bayesian Methods in Computational Many-Body Physics. In: Ainsworth, T.L., Campbell, C.E., Clements, B.E., Krotscheck, E. (eds) Recent Progress in Many-Body Theories. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-3466-2_26
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DOI: https://doi.org/10.1007/978-1-4615-3466-2_26
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