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New directions in topological phases: from fractons to spatial symmetries: April 13-17, 2020

Organized by Jennifer Cano, Dominic Else, Andrey Gromov, Siddharth Parameswaran, and Yizhi You

Topological phases of matter are a long-standing subject of interest in the condensed matter community, and increasingly relevant to issues in high-energy physics.

A topological phase is traditionally defined to be a gapped phase which is “non-trivial” (cannot be deformed to a trivial insulator without a phase transition), but where the non-triviality cannot be ascribed merely to spontaneous symmetry breaking.

Several years ago, a conceptually new type of gapped phases was discovered. These phases are known as fracton phases, due to the presence of topologically non-trivial excitations that can only move on lower-dimensional submanifolds, or cannot move at all. Fracton phases challenge our notion of “topological order”, because the low-energy theory depends on some non-topological features of space. In fact, these phases also appear to have an intricate relationship with the geometry of the space where they reside. Alternatively, these phases can be viewed as higher-rank gauge theories obtained by gauging the subsystem symmetries — the symmetries which act along lower-dimensional subspaces. Fractons have attracted a broad interdisciplinary interest due to their potential relationship to lattice gauge theory, quantum computation and memory, elasticity, glassy dynamics and emergent gravity in condensed matter.

Meanwhile, another kind of topological phase which depends on the geometry of space is crystalline topological phases, which are topological phases of matter with spatial symmetries. General approaches to such phases have recently begun to emerge. In many cases they have novel edge states, such as the “higher-order topological insulators”.

The workshop will concentrate on discussing the new developments and ideas regarding the fracton phases and other closely related topics such as topological phases with spatial or subsystem symmetries, as well as higher order topological phases.

This workshop is associated with the program:

Geometrical aspects of topological phases of matter: spatial symmetries, fractons and beyond: April 13-June 5, 2020, 2019