title: Numerical optimization using flow equations.
abstract: We develop a method for multidimensional optimization using flow equations. This method is based on homotopy continuation in combination with a maximum entropy approach. Extrema of the optimizing functional correspond to fixed points of the flow equation. While ideas based on Bayesian inference such as the maximum entropy method always depend on a prior probability, the additional step in our approach is to perform a continuous update of the prior during the homotopy flow. The prior probability thus enters the flow equation only as an initial condition. We demonstrate the applicability of this optimization method for two paradigmatic problems in theoretical condensed matter physics: numerical analytic continuation from imaginary to real frequencies and finding (variational) ground states of frustrated (quantum) Ising models with random or long-range antiferromagnetic interactions.
authors.affiliation: Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria, and Institute for Quantum Optics and Quantum Information, 6020 Innsbruck, Austria.
authors.forename: Matthias
authors.initials: M
authors.lastname: Punk