# Dual Boson approach with instantaneous interaction

## TL;DR

This paper introduces a simplified version of the Dual Boson approach by enforcing an instantaneous interaction, which preserves key physical laws and accurately captures certain phase transitions in strongly correlated systems.

## Contribution

It develops a static interaction variant of the Dual Boson method, maintaining charge conservation and physical consistency, suitable for multiband systems.

## Key findings

- Enforces absence of phase transitions in finite systems
- Respects the Mermin-Wagner theorem in 2D systems
- Captures metal to charge ordered phase transition accurately

## Abstract

The Dual Boson approach to strongly correlated systems generally involves a dynamic (frequency-dependent) interaction in the auxiliary impurity model. In this work, we explore the consequences of forcing this interaction to be instantaneous (frequency-independent) via the use of a self-consistency condition on the instantaneous susceptibility. The result is a substantial simplification of the impurity model, especially with an eye on realistic multiband implementations, while keeping desireable properties of the Dual Boson approach, such as the charge conservation law, intact. We show and illustrate numerically that this condition enforces the absence of phase transitions in finite systems, as should be expected from general physical considerations, and respects the Mermin-Wagner theorem. In particular, the theory does not allow the metal to insulator phase transition associated with the formation of the magnetic order in the two-dimensional system. At the same time, the metal to charge ordered phase transition is allowed, as it is not associated with the spontaneous breaking of a continuous symmetry, and is accurately captured by the introduced approach.