Holographic Checkerboards

TL;DR

This paper constructs and analyzes holographic black brane solutions exhibiting spontaneous checkerboard order, revealing phase transitions and instabilities relevant for understanding spatially modulated phases in strongly coupled field theories.

Contribution

It introduces a numerical construction of cohomogeneity-three black branes with checkerboard order, including phase transition analysis and instability characterization.

Findings

Checkerboard phases form spontaneously without explicit lattices.

First-order phase transition between checkerboard and stripe phases.

Identification of spatially modulated instabilities in AdS black branes.

Abstract

We construct cohomogeneity-three, finite temperature stationary black brane solutions dual to a field theory exhibiting checkerboard order. The checkerboards form a backreacted part of the bulk solution, and are obtained numerically from the coupled Einstein-Maxwell-scalar PDE system. They arise spontaneously and without the inclusion of an explicit lattice. The phase exhibits both charge and global U(1)-current modulation, which are periodic in two spatial directions. The current circulates within each checkerboard plaquette. We explore the competition with striped phases, finding first-order checkerboard to stripe phase transitions. We also detail spatially modulated instabilities of asymptotically AdS black brane backgrounds with neutral scalar profiles, including those with an hyperscaling violating IR geometry at zero temperature.