[PhD Thesis Presentation] - Mr. Han Yan "Fracton States of Matter:From Holography to Frustrated Magnetis"

Presenter: Mr. Han Yan

Supervisor: Professor Nic Shannon

Co-Supervisor: Professor Hirotaka Sugawara

Unit: Theory of Quantum Matter Unit

Title: Fracton States of Matter:From Holographyto Frustrated Magnetis

Abstract:

The discipline of modern condensed matter physic has a lot ambitions: to discover all possible quantum phases of matter, to study the exotic properties and applications of different matter states, and to realize them in experiments. A recent exciting develop- ment in this field is the discovery of the fracton states of matter. Featuring immobile excitations and gauged/ungauged subsystem symmetries, it is a phase of quantum many-body systems that transcend the traditional scenarios of Landau-Ginsberg sym- metry breaking and topological quantum states.

This thesis is devoted to a few aspects of the fracton states of matter. First, we study a unique property of the fracton models: they mimic the quantum-informational fea- tures of gravity. This can be shown in the context of holographic principle or AdS/CFT duality: a fracton model in AdS space can be shown to satisfy the major properties of holography: the boundary entanglement entropy satisfies Ryu-Takayanagi formula, and the bulk reconstruction follows the Rindler reconstruction. Furthermore, the frac- ton model in hyperbolic space is known to be similar to various other toy models of holography including holographic tensor-networks and bit-threads model. The in- triguing similarity between fracton models and gravity, as well as its implications, are discussed at length.

In the second half of the thesis, we explore possible experimental routes to realize the fracton phases. Here we focus on frustrated magnets on the pyrochlore lattice, one of the most versatile and experimentally fruitful framework to realize spin liquids. By analyzing the symmetry and the coarse-grained limit of the model, we find it possible to realize various versions of rank-2 U(1) gauge theory, in models motivated by real materials.