Transverse field spin models: From Statistical Physics to Quantum Information

Details Transverse field spin models: From Statistical Physics to Quantum Information Transverse field spin models: From Statistical Physics to Quantum Information

2010-12-03

arxiv.org/abs/1012.0653v1

Physics

Condensed Matter

Statistical Mechanics

Submitted (Over-sized!) version of the commissioned review article for Reviews of Modern Physics

Scientific paper

We review quantum phase transitions in spin systems in transverse fields taking the examples of some paradigmatic models, namely, the spin-1/2 Ising and $XY$ models in a transverse field in one and higher spatial dimensions. Beginning with a brief overview of quantum phase transitions, we introduce the model Hamiltonians and discuss the mean field studies. We then provide exact solutions in one spatial dimension connecting them to conformal field theoretical studies. We also discuss Kitaev models and quantum rotor models in these contexts. The equivalence of the quantum phase transitions in these models to finite temperature phase transitions of higher dimensional classical models is also discussed. Studies of the quantum phase transitions in the presence of quenched randomness and with frustrating interactions are also presented at some length. Next, we turn to more recent topics like information theoretic measures of the quantum phase transitions in these models and non-equilibrium dynamics across a variety of quantum critical points and lines. Finally, recent experimental studies of transverse Ising-like systems are summarized in the concluding section.

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