An Introduction to Exotic Phases of Matter By Tyler D Ellison - PowerPoint PPT Presentation

An Introduction to Exotic Phases of Matter By Tyler D Ellison

Outline 1. Vague statements about phases of matter 2. Entanglement 3. Classification of exotic quantum phases of matter 1. A few words about long-range entanglement 2. More words about short-range entanglement 4. SPT phases 5. Open questions

Vague statements about phases of matter

Vague statements about phases of matter

Vague statements about phases of matter A metal A magnet Disordered An insulator

Vague statements about phases of matter Quantum entanglement

Entanglement Total Hilbert space: A basis for :

Entanglement A basis for :

Entanglement New Hilbert space: Trivial product state:

Entanglement

Classification of exotic quantum phases of matter • Can focus on ground states if Niveditha Ram • Hamiltonian is gapped in the thermodynamic limit • At zero temperature Thermodynamic limit Energy

Classification of exotic quantum phases of matter † † † † † † † † † † † † †

Classification of exotic quantum phases of matter † † † † † † † †

Classification of exotic quantum phases of matter … … … Long-range entanglement: Toric code • … … or … … String-net models • Fractional quantum Hall systems • Anyons • Short-range entanglement: Topological insulators • … … Topological superconductors • Haldane phase •

SPT phases “Trivial states”

SPT phases † † † † † † † † † † † † †

SPT phases Protecting symmetry: G

Some questions currently on my mind • What is the structure of the quantum circuits that build topological insulator states? • Do topological insulators admit frustration-free strictly local commuting projector Hamiltonians?

Image Sources Phase diagram of water: https://en.wikipedia.org/wiki/Phase_diagram#/media/File:Phase_diagram_of_water.svg Quantum entanglement: http://gizmodo.com/scientists-break-quantum-record-entangling-3-000-atoms-1694832887

Thanks!

Current problems Topological insulator Vacuum

Current problems Protecting symmetry: particle number conservation, U(1) and time-reversal invariance, T

Current problems

Current problems Protecting symmetry: G

Current problems Protecting symmetry: particle number conservation, U(1) and time-reversal invariance, T

H Classification of phases -- Hamiltonians H H H H H H H H H H H H H H H H H H H H H H H

SPT phases † † † † † † † † † † † † †