The quantum Ising chain for beginners
Glen Bigan Mbeng, Angelo Russomanno, Giuseppe E. Santoro
SciPost Phys. Lect. Notes 82 (2024) · published 14 June 2024
- doi: 10.21468/SciPostPhysLectNotes.82
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Abstract
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 analyze 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.
Cited by 5
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Authors / Affiliations: mappings to Contributors and Organizations
See all Organizations.- 1 Glen Bigan Mbeng,
- 2 Angelo Russomanno,
- 3 4 5 Giuseppe E. Santoro
- 1 Universität Innsbruck / University of Innsbruck [UBI]
- 2 Università degli Studi di Napoli Federico II / University of Naples Federico II
- 3 Scuola Internazionale Superiore di Studi Avanzati / International School for Advanced Studies [SISSA]
- 4 International Centre for Theoretical Sciences [ICTS-TIFR]
- 5 Istituto Officina dei Materiali / Materials Foundry Institute [IOM]
- Horizon 2020 (through Organization: European Commission [EC])
- Ministero dell'Università e della Ricerca