Citation: Pretko, Michael, and Leo Radzihovsky. "Fracton-elasticity duality." Physical review letters 120.19 (2018): 195301.
Web: https://arxiv.org/abs/1711.11044
Tags: Physical
In this lovely paper, the authors demonstrate a precise mathematical duality between the standard theory of topological defects in (quantum) crystals to the new gauge theory of fractons. This has several immediate implications. (1) It gives a lovely semi-classical picture for fractions. The fact that topological lattice defects have restricted mobility is a standard feature of elasticity theory, and can be seen directly on the lattice - this duality shows that this really is the same phenomenon as fractons. (2) It allows one to understand certain fracton gauge theories much better; by passing to elasticity theory and using the well-understood phase diagram for quantum crystals one can predict a phase diagram for some fracton gauge theories. (3) It gives a natural setting for the application of fractions to systems of more conventional interest.
At a coarse level, this duality arises from a series of change of variables, and reordering of integrals.
What's so cute about precise mathematical dualities is that even the smaller features of the theories line up. For instance, the transverse and longitudinal phonons in the crystal correspond to the two gapless gauge modes of the fracton gauge theory. As the authors put it: "this work opens the door for the future exchange of ideas between the emerging field of fractons and the well-established study of elasticity theory".