# Negative electron compressibility in the Hubbard Model

## TL;DR

This study investigates negative electron compressibility in the 2D Hubbard model using strong coupling diagrams, revealing phase separation near certain chemical potentials at low temperatures.

## Contribution

It introduces a detailed diagrammatic analysis of electron interactions in the Hubbard model, highlighting negative compressibility and phase separation regions.

## Key findings

- Negative compressibility occurs for μ<0 and μ>U at low temperatures.
- States with phase separation emerge near these regions at even lower temperatures.
- The strong coupling diagram technique effectively captures electron fluctuation effects.

## Abstract

Using the strong coupling diagram technique, we study the one-band repulsive Hubbard model on a two-dimensional square lattice in a wide range of chemical potentials $\mu$. Infinite sequences of diagrams describing interactions of electrons with spin and charge fluctuations are taken into account. At low temperatures, regions of the negative electron compressibility are found for $\mu<0$ and $\mu>U$, where $U$ is the Hubbard repulsion. For even lower temperatures, in the neighborhood of these regions, states with the phase separation are revealed.