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Quantum Physics in One Dimension$
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Thierry Giamarchi

Print publication date: 2003

Print ISBN-13: 9780198525004

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198525004.001.0001

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(p.160) 6 SPIN 1/2 CHAINS
Quantum Physics in One Dimension

Thierry Giamarchi

Oxford University Press

This chapter examines the question of spin systems, the simplest realization of Luttinger liquids. The peculiarities of one dimension make the solution of this problem quite surprising and different from what our intuition expects based on a classical vision of the spins. The spin 1/2 chain and its physical properties are discussed, along with the use of one-dimensional interacting fermions to solve the spin chain problem. The ideal spin 1/2 chain can be perturbed in many ways. Each of these perturbations can lead to some quite rich physics. This chapter considers the simplest of them, perturbations that apply to strictly one-dimensional chains, and examines coupling between chains.

Keywords:   spin 1/2 chains, Hamiltonian, bosonization, finite magnetic fields, coupled chains, spin-Peierls, one dimension

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