The quantum Ising chain for beginners

Mbeng, Glen Bigan; Russomanno, Angelo; Santoro, Giuseppe E.

doi:10.21468/SciPostPhysLectNotes.82

SciPost Physics Lecture Notes

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.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysLectNotes.82
TI  - The quantum Ising chain for beginners
PY  - 2024/06/14
UR  - https://scipost.org/SciPostPhysLectNotes.82
JF  - SciPost Physics Lecture Notes
JA  - SciPost Phys. Lect. Notes
SP  - 82
A1  - Mbeng, Glen Bigan
AU  - Russomanno, Angelo
AU  - Santoro, Giuseppe E.
AB  - 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.
ER  -

@Article{10.21468/SciPostPhysLectNotes.82,
	title={{The quantum Ising chain for beginners}},
	author={Glen Bigan Mbeng and Angelo Russomanno and Giuseppe E. Santoro},
	journal={SciPost Phys. Lect. Notes},
	pages={82},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhysLectNotes.82},
	url={https://scipost.org/10.21468/SciPostPhysLectNotes.82},
}

Cited by 7

Authors / Affiliations: mappings to Contributors and Organizations

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¹ Glen Bigan Mbeng,
² Angelo Russomanno,
³ ⁴ ⁵ Giuseppe E. Santoro

Funders for the research work leading to this publication

Horizon 2020 (through Organization: European Commission [EC])
Ministero dell'Università e della Ricerca