2010/12/31 by Subir Sachdev · 1 citation
Physics and Astronomy · #Advanced Condensed Matter Physics #Antiferromagnetism #Atomic orbital #Condensed matter physics #Fermi liquid theory #Gauge theory #Hexagonal lattice #Hubbard model #Lattice (music) #Lattice field theory #Lattice gauge theory #Mott insulator #Physics #Physics of Superconductivity and Magnetism #Quantum mechanics #Quantum spin liquid #Quantum, superfluid, helium dynamics #Theoretical physics #Valence bond theory #cond-mat.str-el #hep-th
paper · pdf · doi:10.1142/9789814350525_0009
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
arxiv created 2011/04/29 · openalex publication_date 2011/11/01 · arxiv updated 2017/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.