Many Phases of Generalized 3D Instanton Crystals

TL;DR

This paper explores the complex phase structure of three-dimensional instanton crystal formations in holographic nuclear matter, revealing diverse lattice and orientation patterns through simulations and analytical methods.

Contribution

It introduces a detailed analysis of instanton crystal structures and orientations in holographic nuclear matter, including simulation results and phase diagram characterization.

Findings

Identification of various ferromagnetic and antiferromagnetic crystal phases

Discovery of non-Abelian crystals with diverse orientation patterns

Complex phase diagram with face-centered-cubic, hexagonal, and simple cubic variants

Abstract

Nuclear matter at large number of colors is necessarily in a solid phase. In particular holographic nuclear matter takes the form of a crystal of instantons of the flavor group. In this article we initiate the analysis of the three-dimensional crystal structures and the orientation patterns for the two-body potential that follows from holographic duality. The outcome of the analysis includes several unexpected results. We perform simulations of ensembles of O(10000) instantons whereby we identify the lattice structure and orientations for the different values of the weight factors of the non-Abelian orientation terms in the two-body potential. The resulting phase diagram is surprisingly complex, including a variety of ferromagnetic and antiferromagnetic crystals with various global orientation patterns, and various "non-Abelian" crystals where orientations have no preferred direction. The latter include variants of face-centered-cubic, hexagonal, and simple cubic crystals which may have remarkably large or small aspect ratios. The simulation results are augmented by analytic analysis of the long-distance divergences, and numerical computation of the (divergence free) energy differences between the non-Abelian crystals, which allows us to precisely determine the structure of the phase diagram.