Abstract

Fractional excitations are well known in one dimension, in polyacetylene, and in two dimensions, in the fractional quantum Hall effect. It was widely believed that three-dimensional models could not support fractional excitations, since the fractionalization of charge in one- and two-dimensional electronic liquids seemed to be intimately linked to the fractional quantum statistics found in lower dimension.

Recently, however, a spectacular example of fractionalization in three dimensions has emerged, in the form of magnetic monopoles in spin ice [1,2]. These monopoles act as independent, point-like sources of magnetic field, and as such are deconfined, fractional excitations. But they are also, by construction, classical entities.

In this talk I present numerical evidence that a closely related class of three-dimensional quantum models can also support such fractional excitations in three dimensions [3]. The most interesting of these models is a ``quantum ice’’ which provides a description of the tunneling of protons in water ice or, equivalently, the quantum dynamics at low temperature in spin ice.

[1] C. Castelnovo et al., Nature (London) 451, 42 (2008) [2] S. Bramwell et al., Nature (London) 461, 956 (2009) [3] O. Sikora et al., Phys. Rev. Lett. 103, 247001 (2009)