ID: 2009.09208

The quantum Ising chain for beginners

September 19, 2020

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Glen Bigan Mbeng, Angelo Russomanno, Giuseppe E. Santoro
Quantum Physics
Condensed Matter
Quantum Gases

We present here various techniques to work with clean and disordered quantum Ising chains, for the benefit of students and non-experts. Starting from the Jordan-Wigner transformation, which maps spin-1/2 systems into fermionic ones, we review some of the basic approaches to deal with the superconducting correlations that naturally emerge in this context. In particular, we analyse the form of the ground state and excitations of the model, relating them to the symmetry-breaking physics, and illustrate aspects connected to calculating dynamical quantities, thermal averages, correlation functions and entanglement entropy. A few problems provide simple applications of the techniques.

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