# Competition between Phase Separation and Spin Density Wave or Charge Density Wave Order: Role of Long-Range Interactions

## TL;DR

This paper uses Quantum Monte Carlo simulations to study how long-range electron-electron interactions influence the competition between phase separation and ordered phases like spin or charge density waves, revealing conditions for stable homogeneous phases.

## Contribution

It demonstrates that incorporating long-range interactions stabilizes homogeneous phases, allowing analysis of momentum-dependent electron-phonon effects beyond phase separation regimes.

## Key findings

- Long-range interactions prevent phase separation in certain models.
- Stable homogeneous phases are identified with specific interaction parameters.
- Phase boundaries between different orders are mapped out.

## Abstract

Recent studies of pairing and charge order in materials such as FeSe, SrTiO$_3$, and 2H-NbSe$_2$ have suggested that momentum dependence of the electron-phonon coupling plays an important role in their properties. Initial attempts to study Hamiltonians which either do not include or else truncate the range of Coulomb repulsion have noted that the resulting spatial non-locality of the electron-phonon interaction leads to a dominant tendency to phase separation. Here we present Quantum Monte Carlo results for such models in which we incorporate both on-site and intersite electron-electron interactions. We show that these can stabilize phases in which the density is homogeneous and determine the associated phase boundaries. As a consequence, the physics of momentum dependent electron-phonon coupling can be determined outside of the trivial phase separated regime.