Machine learning is used to extract essential pattern from big data. This technique can be used to extract the essential feature of quantum many-body wave function (=a vector with exponentially large dimensions), and to obtain compact representation of many-body states. In this article, we review representations of many-body states using Boltzmann machine, a type of artificial neural network. We introduce an efficient representation using restricted Boltzmann machines (RBM) and also discuss the efforts to improve the RBM wave functions.
The highly “electron-electron” correlated researches have been vigorously developed in π-, d-, and f-electron systems. Moreover, “electron-proton” coupled studies have attracted much attentions in π-electron based organic crystals. In this review, the basic model, room-temperature ferroelectricity, and novel phenomena of conductivities and magnetism by electron-proton coupling in organic crystals were introduced. Especially, the π-electron based quantum spin liquid state coupled with quantum fluctuation of protons in hydrogen bonds and the switching of conductivity and magnetism triggered by the disorder-order transition of deuterium in hydrogen-bonds have been reported as novel proton-electron coupling properties. Moreover, these phenomena with dynamical π-electron-proton coupling can be controlled by external stimuli such as pressure and electric field.
The study of the orbital angular momentum and edge current in chiral superfluids/superconductors has been controversial. They strongly depend on details of sample boundaries and shapes, and hence experimental setups. Such dependences do not contradict the standard thermodynamics, and orbital angular momentum and edge current are not bulk intrinsic properties of a chiral superfluid/superconductor. We discuss basic properties of these quantities.