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Other version: http://www.oxfordscholarship.com/view/10.1093/acprof:oso/9780199661886.001.0001/acprof9780199661886
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Title 
Strongly correlated bosons and fermions in optical lattices 

Authors  
Published in  Salomon, C. & Shlyapnikov, G. V. & Cugliandolo, L. F. ManyBody Physics with Ultracold Gases. Oxford: Oxford University Press. 2012  
Collection 
Lecture Notes of the Les Houches Summer School; 94 

Abstract  This chapter gives an introduction to the physics of interacting quantum systems, both bosonic and fermionic. Section 1.2 introduces the physics of quantum particles in periodic lattices. Section 1.3 examines, for the case of bosons, how the combined effects of lattice and interaction can turn the system into an insulator, the socalled Mott insulator, and discusses the corresponding physics. Section 1.4 discusses what happens when the system is onedimensional. Section 1.5 moves on to the case of fermions. It discusses first Fermiliquid theory and the concept of quasiparticles, Landau’s description of the lowenergy excitations of interacting fermion systems. Section 1.6 shows how, like the method for bosons, the combination of a lattice and strong interactions can turn a Fermi liquid into a Mott insulator. Section 1.7 looks at the properties of onedimensional fermions, shows how Fermi liquid theory fails because lowenergy excitations are now collective modes instead of quasiparticles, and examines the corresponding physics for both the conducting and insulating phases. Finally, Section 1.8 draws some conclusions and give some perspectives.  
Keywords  Quantum systems — Quantum particles — Periodic lattices — Bosons — Mott insulator — Fermions — Fermi liquids — Quasiparticles — Landau  
Identifiers  ISBN: 9780199661886  
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Citation (ISO format)  GEORGES, Antoine, GIAMARCHI, Thierry. Strongly correlated bosons and fermions in optical lattices. In: Salomon, C. & Shlyapnikov, G. V. & Cugliandolo, L. F. (Ed.). ManyBody Physics with Ultracold Gases. Oxford : Oxford University Press, 2012. (Lecture Notes of the Les Houches Summer School; 94) https://archiveouverte.unige.ch/unige:35899 