Holographic discommensurations

TL;DR

This paper explores the phase transition between commensurate and incommensurate states in a holographic model, focusing on the role of discommensurations as solitonic objects and their proliferation.

Contribution

It introduces a holographic approach to understanding discommensurations and the commensurate/incommensurate phase transition through soliton proliferation.

Findings

Discommensurations are characterized as solitonic objects in the model.

The phase transition is explained as a proliferation of discommensurations.

Numerical techniques for studying these phenomena are discussed.

Abstract

When the system with internal tendency to a spontaneous formation of a spatially periodic state is brought in contact with the external explicit periodic potential, the interesting phenomenon of commensurate lock in can be observed. In case when the explicit potential is strong enough and its period is close to the period of the spontaneous structure, the latter is forced to assume the periodicity of the former and the commensurate state becomes a thermodynamically preferred one. If instead the two periods are significantly different, the incommensurate state is formed. It is characterized by a finite density of solitonic objects -- discommensurations -- on top of the commensurate state. In this note I study the properties of discommensurations in holographic model with inhomogeneous translational symmetry breaking and explain how one can understand the commensurate/incommensurate phase transition as a proliferation of these solitons. Some useful numerical techniques are discussed in the Appendix.