Strongly correlated low-dimensional systems

Low dimensional systems often exhibit strong quantum fluctuation effects leading to the failure of conventional theories. This creates theoretical challenges which can sometimes be met using field theory, integrability and numerical techniques such as the Density Matrix Renormalization Group and Matrix Product States that are especially powerful in one dimension. Improving experimental techniques and the synthesis of new materials are leading to increasing numbers of experimental realizations of these low dimensional models.

Current projects include:

  • He-4 Luttinger liquids in nanopores
  • Systems of interacting Majorana modes in 1 and 2 dimensions
  • SU(n) spin systems that can be realized by cold atoms
  • field-induced phase transitions in low dimensional antiferromagnets
  • ferromagnetism on edges of graphene nano-ribbons

Quantum Impurities

Models of a localized degree of freedom interacting with a continuum of gapless excitations occur in various areas of condensed matter physics. They can describe a magnetic impurity interacting with conduction electrons in a metal (the Kondo model) or a gated semi-conductor quantum dot connected to metallic leads or a localized Majorana mode interacting with normal electrons. Insight from such single-impurity models is often extrapolated to describe compounds such as heavy fermions which contain a regular array of magnetic ions. Such models also form the basis of the dynamical mean field theory approach to strongly interacting bulk systems. The Numerical Renormalization Group technique can be applied to these models. Boundary conformal field theory provides exact solutions to non-Fermi liquid critical points occurring in them.

Current projects include:

  • Interaction effects in topological superconductor – normal junctions
  • Kondo effect in graphene

Principal investigator

Ian Affleck (UBC)

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