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Title: Berry Flux Diagonalization: Application to electric polarization
Abstract: The electric polarization is a key quantity in characterizing how a system interacts with an electric field and is thus relevant in a variety of contexts from ferroelectric switching to strong light-matter interactions. The mathematics of Berry phases and related concepts needed to compute the electric polarization in crystal systems are also connected to a broader range of physical phenomena such as the quantum hall effect and theoretical techniques such as Wannierization.
In this talk I will present a first principles approach for predicting changes in Berry phases which has been applied to compute the
switching polarization of ferroelectrics. It is straightforward to compute this change of phase modulo $2\pi$ using existing techniques, but a branch choice is then required to specify the predicted switching polarization. While in the most general case the resolution of this branch choice requires knowledge of the path along which the system switches we note that good agreement with experiment can be obtained by assuming a path which involves minimal evolution of the state. To
compute the change along a generic minimal path, we decompose the change of Berry phase into many small contributions, each much less than $2\pi$, allowing for a natural resolution of the branch choice. We show that for typical ferroelectrics, including those that would have otherwise required a densely sampled path, this technique allows the switching polarization to be computed without any need for intermediate sampling between oppositely polarized states. Potential applications and generalizations of the technique beyond ferroelectric switching will also be discussed.