Minimally packed phases in holography

TL;DR

This paper constructs holographic models of black branes with spontaneous lattice formation, revealing minimal packing structures like the triangular lattice as thermodynamically favored, and explores their properties at various temperatures.

Contribution

It introduces a numerical construction of holographic lattice phases with minimal packing structures and analyzes their thermodynamic and stress tensor properties.

Findings

Triangular lattice minimizes free energy at specific magnetic fields.

The average stress tensor resembles that of a perfect fluid.

Crystalline ground states persist at low temperatures.

Abstract

We numerically construct asymptotically AdS black brane solutions of $D=4$ Einstein-Maxwell theory coupled to a pseudoscalar. The solutions are holographically dual to $d=3$ CFTs at finite chemical potential and in a constant magnetic field, which spontaneously break translation invariance leading to the spontaneous formation of abelian and momentum magnetisation currents flowing around the plaquettes of a periodic Bravais lattice. We analyse the three-dimensional moduli space of lattice solutions, which are generically oblique, and show, for a specific value of the magnetic field, that the free energy is minimised by the triangular lattice, associated with minimal packing of circles in the plane. We show that the average stress tensor for the thermodynamically preferred phase is that of a perfect fluid and that this result applies more generally to spontaneously generated periodic phases. The triangular structure persists at low temperatures indicating the existence of novel crystalline ground states.