Hall Number of Strongly Correlated Metals

Area of Science:

• Condensed matter physics
• Quantum mechanics
• Materials science

Background:

• The Hall number is a crucial transport coefficient in understanding electronic properties of materials.
• Calculating the Hall number, especially in strongly correlated systems, presents significant theoretical and computational challenges.
• Existing methods often struggle with arbitrary potentials and interactions, limiting applicability.

Purpose of the Study:

• To derive an exact formula for the temperature-dependent Hall number.
• To establish a connection between the Hall number and equilibrium susceptibilities.
• To demonstrate the formula's utility in complex systems like Mott phases.

Main Methods:

• Derivation of an exact analytical formula for the Hall number.
• Utilizing theoretical frameworks applicable to nonrelativistic fermions and bosons.
• Employing equilibrium susceptibilities as a key calculational component.

Main Results:

• An exact formula for the temperature-dependent Hall number is established.
• The formula demonstrates that the Hall number depends solely on equilibrium susceptibilities.
• The approach is shown to be more numerically tractable than direct conductivity calculations.
• The Hall sign near Mott phases of lattice bosons is successfully calculated.

Conclusions:

• The derived formula provides a powerful new tool for calculating the Hall number in diverse materials.
• Linking the Hall number to equilibrium susceptibilities simplifies theoretical investigations, particularly for strongly correlated systems.
• This work opens avenues for more efficient numerical studies of electronic transport phenomena.