# The Inhomogeneous Phase of Dense Skyrmion Matter

## TL;DR

This paper quantitatively confirms that dense skyrmion matter at low density forms an inhomogeneous phase with lumps, revealing a complex phase diagram and properties similar to nuclear matter.

## Contribution

It introduces a mathematical model of inhomogeneous skyrmion phases using the 't Hooft instanton and Atiyah-Manton ansatz, providing new insights into their structure and phase transitions.

## Key findings

- Inhomogeneous skyrmion phase is stable at low density.
- Skyrmion matter develops a skin and exhibits properties akin to nuclear matter.
- The phase diagram is more complex than a simple transition between crystal phases.

## Abstract

It was predicted qualitatively in ref.[1] that skyrmion matter at low density is stable in an inhomogeneous phase where skyrmions condensate into lumps while the remaining space is mostly empty. The aim of this paper is to proof quantitatively this prediction. In order to construct an inhomogeneous medium we distort the original FCC crystal to produce a phase of planar structures made of skyrmions. We implement mathematically these planar structures by means of the 't Hooft instanton solution using the Atiyah-Manton ansatz. The results of our calculation of the average density and energy confirm the prediction suggesting that the phase diagram of the dense skyrmion matter is a lot more complex than a simple phase transition from the skyrmion FCC crystal lattice to the half-skyrmion CC one. Our results show that skyrmion matter shares common properties with standard nuclear matter developing a skin and leading to a binding energy equation which resembles the Weiszaecker mass formula.