Strongly correlated bosons and fermions in optical lattices

Antoine Georges and Thierry Giamarchi

in Many-Body Physics with Ultracold Gases

Published in print November 2012 | ISBN: 9780199661886
Published online January 2013 | e-ISBN: 9780191748356 | DOI:

Series: Lecture Notes of the Les Houches Summer School

Strongly correlated bosons and fermions in optical lattices

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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 so-called Mott insulator, and discusses the corresponding physics. Section 1.4 discusses what happens when the system is one-dimensional. Section 1.5 moves on to the case of fermions. It discusses first Fermi-liquid theory and the concept of quasi-particles, Landau’s description of the low-energy 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 one-dimensional fermions, shows how Fermi liquid theory fails because low-energy excitations are now collective modes instead of quasi-particles, 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; quasi-particles; Landau

Chapter.  31723 words.  Illustrated.

Subjects: Atomic, Molecular, and Optical Physics

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