The Landscape of the Hubbard Model
نویسنده
چکیده
I present a pedagogical survey of a variety of quantum phases of the Hubbard model. The honeycomb lattice model has a conformal field theory connecting the semi-metal to the insulator with Néel order. States with fractionalized excitations are linked to the deconfined phases of gauge theories. I also consider the confining phases of such gauge theories, and show how Berry phases of monopoles induce valence bond solid order. The triangular lattice model can display a metal-insulator transition from a Fermi liquid to a deconfined spin liquid, and I describe the theory of this transition. The bilayer triangular lattice is used to illustrate another compressible metallic phase, the ‘fractionalized Fermi liquid’. I make numerous connections of these phases and critical points to the AdS/CFT correspondence. In particular, I argue that two recent holographic constructions connect respectively to the Fermi liquid and fractionalized Fermi liquid phases. TASI Lectures (Boulder, June 2010) Chandrasekhar Lecture Series and Discussion Meeting on ‘‘Strongly Correlated Systems and AdS/CFT’’ (International Center for Theoretical Science (ICTS), Bangalore, Dec 2010) 1 ar X iv :1 01 2. 02 99 v5 [ he pth ] 29 A pr 2 01 1
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