Hall Number of Strongly Correlated Metals

An exact formula for the temperature dependent Hall number of metals is derived. It is valid for nonrelativistic fermions or bosons, with an arbitrary potential and interaction. This dc transport coefficient is proven to (remarkably) depend solely on equilibrium susceptibilities, which are more amenable to numerical algorithms than the conductivity. An application to strongly correlated phases is demonstrated by calculating the Hall sign in the vicinity of Mott phases of lattice bosons.

Figure 1

The orthonormal Krylov bases, Eq. (19), constructed (for $B=0$) from $j^x$ and $j^y$ by repeated application of the Liouvillian $\mathcal{L}$. ${\mathrm{\Delta }}_n$ are the recurrents of ${\sigma }_{xx}$. $M_{n,m}^{\prime \prime }$ are the magnetization matrix elements defined in Eq. (23).

Figure 2

Hall signs in the strong interactions regime of the Bose Hubbard model Eq. (28). Mott insulators are the thick black lines, ending at critical points (black circles). The solid blue lines mark the Hall sign changes at zero temperature, computed by Huber and Lindner [9]. At high temperatures, we find the same sign changes using quantum rotators, and HCB in Eqs. (32) and (36).