The Hall number across a van Hove singularity

In the context of the relaxation time approximation to Boltzmann transport theory, we examine the behavior of the Hall number, $n_H$, of a metal in the neighborhood of a Lifshitz transition from a closed Fermi surface to open sheets. We find a universal non-analytic dependence of $n_H$ on the electron density in the high field limit, but a non-singular dependence at low fields. The existence of an assumed nematic transition produces a doping dependent $n_H$ similar to that observed in recent experiments in the high temperature superconductor YBa$_2$Cu$_3$O$_{7-x}$.
Comment: References added, text modified to include extended discussion of the modified Figure 4. 5 pages, 4 figures, with 13 pages of Supplemental Material