CM4: Strongly correlated 1D systems: Luttinger liquids

Module title: Strongly correlated 1D systems: Luttinger liquids (CM4)

Module convenor: Professor Igor Lerner (Birmingham)

Module aims:

This course follows up the Introduction to QFT for CM physics.

In one-dimensional systems both interaction and disorder are crucial: in contrast to higher dimensions, particles cannot avoid each other and are strongly localized even by a small disorder. This makes low-energy elementary excitations in 1D systems very special: they practically never resemble the underlying particles. Landau's Fermi-liquid theory never works for fermions in 1D: instead, the interacting particles form the Luttinger liquid of "plasmons" or "phonons".

Although 1D systems were of great interest for theorists for more than 60 years (with main tools for their description built in 1980's), the experimental realisations were relatively scarce until the end of 1980's (polymers and organic compounds). But since then we witnessed a real burst in 1D experiments: quantum wires, carbon nanotubes, Josephson junction arrays, edge states in Quantum Hall systems, cold atomic Bose or Fermi gases in 1D optical traps. On top of this, properties of many quasi-1D systems (like organic superconductors, various ladder and spin compounds) are mostly defined by their 1D excitations.

The main aim of the course is to describe a set of theoretical tools for studying strongly correlated and disordered 1D systems. The description is based on the QFT language, both in the functional-integral and in the operator approaches.

Syllabus

  • To be added
Duration: 
2hs
Academic year: 
2012-2013
Starts: 
07/01/2013 - 15:00