Project IV (MATH4072) 2015-16


Quantum Phase Transitions

Aristomenis Donos

Description

Quantum phase transitions are transitions that happen at zero temperature while varying an external parameter of a physical system. Such a parameter can be an external magnetic field, charge doping, applied pressure etc. In contrast to thermal phase transitions, it is the low energy, quantum mechanical degrees of freedom that decide about the true ground state.

When such a transition is continuous and not abrupt, it is of fundamental interest to understand the details of the critical point. More interestingly, they are known to have a strong impact on the finite temperature physics and properties of real materials. The most prominent example is the cuprate superconductors and in particular, the strange metallic regime of their phase diagram.

The project will explore the mathematical description and the important consequences of quantum criticality.

Prerequisites

  • Quantum Mechanics III
  • Mathematical Physics II
  • Statistical Mechanics III

Co-requisites

Advanced Quantum Theory IV is not required but is highly recommended.

Resources

Main reading material:
  • Sachdev, Subir (2011). Quantum Phase Transitions. Cambridge University Press. (2nd ed.).
The following article by Volta is also recommended :
  • Vojta, Thomas (2000). "Quantum phase transitions in electronic systems". Annalen der Physik.
  • For a brief introduction to the concepts see Wiki

email: Aristomenis Donos