Entanglement mean-field theory and the Curie-Weiss law

Abstract

The mean-field theory, in its different hues, forms a useful tool for investigating single-body properties, like magnetization and susceptibility, of many-body systems. We propose an “entanglement mean-field theory”, which transforms a many-body system into a two-body one, while retaining footprints of the many-body parent, using which it is possible to examine its two-body properties, and predict temperature-driven as well as quantum fluctuation-driven critical phenomena, by considering two-body self-consistency equations in contrast to single-body ones in mean-field–like theories. Compared to mean-field theory, the proposed one, with little to no extra complicacy, makes better predictions for the critical points, as well as for the qualitative and quantitative behavior of single- and two-body physical quantities. In particular, the predictions of the proposed theory are in much better conformity with the Curie-Weiss law for magnetization. Also, the proposed theory predicts an order by disorder for a correlation function in the random-field transverse quantum Ising model.