The landscape of the Hubbard model

TL;DR

This paper provides a comprehensive pedagogical overview of various quantum phases in the Hubbard model, exploring lattice-specific phenomena, gauge theories, and connections to holography, highlighting recent theoretical advances.

Contribution

It offers a detailed survey of quantum phases in the Hubbard model, including new insights into gauge theories, fractionalization, and holographic connections.

Findings

Identification of conformal field theory connecting semi-metal to insulator on honeycomb lattice

Linking fractionalized excitations to deconfined gauge phases

Connections between Hubbard phases and AdS/CFT holography

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.