The landscape of the Hubbard model
arXiv:1012.0299 · doi:10.1142/9789814350525_0009
Abstract
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 Neel 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.
56 pages, 16 figures; TASI and Chandrasekhar lectures; (v3) expanded discussion of phases with Fermi surfaces; (v5) added section on Mott transition on the triangular lattice
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- What can gauge-gravity duality teach us about condensed matter physics?
- Holographic Fermi and Non-Fermi Liquids with Transitions in Dilaton Gravity
- On Lifshitz scaling and hyperscaling violation in string theory
- Bootstrapping 3D Fermions with Global Symmetries
- Fermi surfaces and gauge-gravity duality
- Conformal field theories in a periodic potential: results from holography and field theory
- A model of a Fermi liquid using gauge-gravity duality
- Multipoint correlators of conformal field theories: implications for quantum critical transport
- Luttinger's theorem, superfluid vortices, and holography
- Quantum Criticality and DBI Magneto-resistance
- The Polyakov Loop of Anti-symmetric Representations as a Quantum Impurity Model
- Large rank Wilson loops in N=2 superconformal QCD at strong coupling
- Integrating Holographic Vector Dominance to Hidden Local Symmetry for the Nucleon Form Factor