# Strong-coupling formula for momentum-dependent susceptibilities in dynamical mean-field theory

## TL;DR

This paper introduces a simplified, computationally efficient formula for calculating momentum-dependent susceptibilities in DMFT, applicable across different coupling regimes, enabling easier evaluation of spin and orbital susceptibilities.

## Contribution

The authors derive a strong-coupling formula for susceptibilities in DMFT that reduces computational cost and is valid in both strong and weak coupling regimes.

## Key findings

- The formula accurately reproduces intersite interactions like kinetic exchange and RKKY.
- Numerical tests show wide applicability including weak-coupling regions.
- Practical approximation levels facilitate easier susceptibility calculations.

## Abstract

Computing momentum-dependent susceptibilities in the dynamical mean-field theory (DMFT) requires solving the Bethe-Salpeter equation, which demands large computational cost. Exploiting the strong-coupling feature of local fluctuations, we derive a simplified formula that can be solved at a considerably lower cost. The validity and the physical meaning of the formula are confirmed by deriving the effective intersite interactions in the strong-coupling limit, such as the kinetic exchange and RKKY interactions. Furthermore, numerical calculations for single-orbital and multiorbital models demonstrate surprisingly wider applicability including weak-coupling region. Based on this formula, we propose three levels of practical approximations that can be chosen depending on complexity of problems. Simpler evaluations of spin and orbital susceptibilities in multiorbital systems thus become possible within DMFT.