Maximum Entropy in Condensed Matter Theory

The principle of maximum entropy has recently been applied to several problems of condensed matter theory. In this paper we discuss some technical aspects of the maxent approach to these problems, and show some general properties of the applications of the method. In particular, we show that maxent can be thought of as a convenient way to close hierarchies, and to extrapolate perturbation series for quantities of physical interest. An illustration of this viewpoint is provided by an examination of the dynamics of a quantum mechanical spin system. We discuss a general maxent method for the extrapolation of power series, and apply the method both to problems of condensed matter (a virial equation of state and spin resonance problems), and to a classic example of a di cult series to handle: the anharmonic quantum oscillator with octic perturbation. We show that the inclusion of information beside Taylor coe cients is critical to obtaining a satisfactory extrapolation for the divergent perturbation series. A general maxent criterion is proposed for optimal series extrapolation.