Ice: a strongly correlated proton system

TL;DR

This paper models proton dynamics in ice using microscopic theories related to Mott insulators, revealing phases like ordered insulators and disordered metallic states, and connects these to experimental ice transitions.

Contribution

It introduces a microscopic model for proton motion in ice, mapping it to gauge theories and identifying phase transitions relevant to ice's physical properties.

Findings

Identification of ordered and disordered phases in proton systems

Mapping of proton dynamics to gauge theories and Ising models

Connection of phase transitions to experimental ice phenomena

Abstract

We discuss the problem of proton motion in Hydrogen bond materials with special focus on ice. We show that phenomenological models proposed in the past for the study of ice can be recast in terms of microscopic models in close relationship to the ones used to study the physics of Mott-Hubbard insulators. We discuss the physics of the paramagnetic phase of ice at 1/4 filling (neutral ice) and its mapping to a transverse field Ising model and also to a gauge theory in two and three dimensions. We show that H3O+ and HO- ions can be either in a confined or deconfined phase. We obtain the phase diagram of the problem as a function of temperature T and proton hopping energy t and find that there are two phases: an ordered insulating phase which results from an order-by-disorder mechanism induced by quantum fluctuations, and a disordered incoherent metallic phase (or plasma). We also discuss the problem of decoherence in the proton motion introduced by the lattice vibrations (phonons) and its effect on the phase diagram. Finally, we suggest that the transition from ice-Ih to ice-XI observed experimentally in doped ice is the confining-deconfining transition of our phase diagram.