The Hall Number of Strongly Correlated Metals
Assa Auerbach
TL;DR
This paper derives an exact, temperature-dependent formula for the Hall number applicable to various particles and interactions, linking it to equilibrium susceptibilities, and demonstrates its use in analyzing strongly correlated phases near Mott insulators.
Contribution
It introduces a novel exact formula for the Hall number that depends only on equilibrium susceptibilities, simplifying analysis of complex correlated systems.
Findings
Derived an exact formula for the temperature-dependent Hall number.
Showed the formula's applicability to strongly correlated phases.
Calculated the Hall sign near Mott phases of lattice bosons.
Abstract
An exact formula for the temperature dependent Hall number of metals is derived. It is valid for non-relativistic fermions or bosons, with 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.
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