The Quantum Ising chain for Beginners
Hands-on Course given by Giuseppe Santoro
Start Date
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I will present various techniques to work with quantum Ising chains. Starting from the Jordan-Wigner transformation, which maps spin-1/2 systems into fermionic ones, we will review some of the basic approaches to deal with the superconducting correlations that naturally emerge in this context. A few problems illustrating important aspects of the physics of this model will provide simple applications of the techniques.

More in detail, the course will consist of:

  • A crash course in scientific programming with python and with jupyter notebooks
  • The Jordan-Wigner transformation applied to one-dimensional spin-1/2 models
  • Free-fermion models (Ising/XY)
  • Translationally invariant and disordered Nambu formalism
  • Time-dependent Bogoljubov-de Gennes equations and calculation of dynamical quantities
  • Calculating thermal averages
  • Calculating correlation functions involving Jordan-Wigner strings
  • Calculating the entanglement entropy 

The course will be strongly ``hands-on based'': collaborating in small groups, we should eventually construct a python library to calculate many properties of Ising spin chains.

Online resources

Filename Size Date Modified
Lecture notes 2.86 MB Thu, 01/11/2024 - 16:48