Holographic Lattices, Dimers, and Glasses

TL;DR

The paper develops a holographic construction of lattices of localized fermionic impurities using a periodic array of D5‑branes in the ${\rm AdS}_5\times S^5$ black brane, enabling thermodynamic quantities to be computed in the large‑$N$, large‑$\lambda$ regime. Doping with anti‑D5‑branes induces dimerization, with a finite‑temperature transition from disconnected to bonded configurations, and the framework yields plateaux in which subsets of lattice bonds dimerize. For a square lattice, the analysis argues a glassy phase at large but finite $N$, characterized by an enormous degeneracy of metastable dimerized states connected only by tunneling, and no long‑range order. The work suggests broad generalizations to other lattices, background geometries, and dynamical hopping, offering a gravity‑dual route to lattice defects, bond ordering, and glassy dynamics in strongly coupled plasmas.

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.

Figures (7)

• Figure 1: Predimerization transition. (a)Disconnected configuration dominates at high temperature. (b)Connected configuration dominates at low temperature.
• Figure 2: $\frac{r_{+}}{L^2}\Delta x$ as a function of ${\tilde{k}}$.
• Figure 3: ${\tilde{F}}_{\rm connected}({\tilde{k}})$ as a function of ${\tilde{k}}$.
• Figure 4: Free energies as functionals of D5 configurations at various temperature ranges. (a)At high temperature, there is only one extremum corresponding to the disconnected solution. (b)At intermediate temperature, there appear two new local extrema corresponding to two connected solutions. (c)At low temperature, the stable connected solution dominates.
• Figure 5: A simple model that experiences the phase transition analogous to the Néel-VBS phase transition.