Quantum complexity in condensed matter physics

S JulianUniversity of Toronto

•Emergent properties•Particle behaviour of fluctuating modes

•Broken symmetry and rigidity•Indirect interaction

Condensed Matter Physics

Fundamental Physics Applied Physics-Quantum properties of many body systems-Noise (eg in electronic circuits)-Novel soft matter, elasticity and viscosity-Modeling the universe

-memory devices for computers-processors for computers-corrosion and catalysis-superconducting devices

energy

time

Elementary particle physics

biologyCondensed matter physics

Combinatorial chemistry vs. emergent properties

Empty boxes are more interesting than people think!

•At 0K: zero point motion

•At Low T: black-body radiation •At high T: electrons and positrons are created

Analogy with quantum condensed matter physics:

•At 0K: zero point motion of phonon, electron-hole pairs, etc.

•At Low T: black-body radiation•Real phonons and electrons+holes

•At high T: electrons and positrons are created

Dispersion relations for (quasi)particles

How to make a metal

Conventional phase transition: broken symmetry states

Conventional phase transition

Spontaneous symmetry breaking The susceptibility diverges

> rigidity

Mass enhancement

Magnetic pairing

Indirect interactions:

- One of the central principles of physics

Unusual “particle-like” excitations are possible in condensed matter systems

Propagating modes

Overdamped modes

The quantum critical point

At Tc, fluctuations diverge

Fe Cu

quantum critical superconductivity?

CePd2Si2 phase diagram

Methodology of condensed matter physics:

• Crystal growth:– Crystals are to us what stars are to astronomers

• Scattering:– A good way to find out what is inside something is to

throw something at it and see how it bounces off• Nano-physics:

– Scanning tunneling microscopy, point contact spectroscopy, etc.

• Low temperatures and high magnetic fields:– Dilution refrigeration

Anvil pressure cells

Phase diagram of Ca2RuO4

Antiferromagetic insulator

Ferromagnetic metal

Pressure / kbar

Tem

pera

ture

/ K

Structural transitions

Atomic orbitals in crystals

Orbital ordering

Summary

• The fundamental principles of quantum condensed matter physics are:– Emergent properties: new kinds of ‘particles’

emerge as complexity increases– Broken symmetry and rigidity– Indirect interactionsThe methodology focuses on crystal growth,

scattering and low temperatures.