Holographic Lattices, Dimers, and Glasses

TL;DR

This paper uses holography to create and analyze a lattice of fermionic impurities in a plasma, revealing dimerization and glassy behavior at low temperatures with a large number of metastable states.

Contribution

It introduces a holographic model of fermionic impurity lattices, explores doping effects, and uncovers glassy phases with metastable configurations at finite N.

Findings

Identification of a critical temperature for dimerization.

Demonstration of glassy behavior in square lattice at large but finite N.

Analysis of metastable dimerized states without long-range order.

Abstract

We holographically engineer a periodic lattice of localized fermionic impurities within a plasma medium by putting an array of probe D5-branes in the background produced by N D3-branes. Thermodynamic quantities are computed in the large N limit via the holographic dictionary. We then dope the lattice by replacing some of the D5-branes by anti-D5-branes. In the large N limit, we determine the critical temperature below which the system dimerizes with bond ordering. Finally, we argue that for the special case of a square lattice our system is glassy at large but finite N, with the low temperature physics dominated by a huge collection of metastable dimerized configurations without long-range order, connected only through tunneling events.