Title: On Landau’s Paradigm for the Classification of Phases

Abstract:

Traditionally, phases of matter have been classified based on spontaneous symmetry breaking—known as Landau’s paradigm. On the other hand, recent theoretical developments, particularly at absolute zero temperature, have established topological approaches to further distinguish phases that share the same symmetry.

In this colloquium, I will discuss the high-pressure phases of water ice, specifically Ice VII and Ice X, as a pedagogical example of this modern perspective. Despite their distinct physical properties, these phases share the same space group and cannot be distinguished by simple symmetry breaking. By mapping the hydrogen bond network to a spin-1 Ising model on a pyrochlore lattice, I will demonstrate how local constraints (the ice rules) give rise to an emergent gauge field and a Coulomb phase characterized by algebraic dipolar correlations.