Everything is a Quantum Ising Model

Despite being a paragon of many-body quantum physics, the quantum Ising model seems restrictive. In particular, all its interactions are classical (i.e., diagonal in an unentangled basis); indeed, quantum fluctuations only enter through a single-site term. Nevertheless, this talk will show that how any qudit Hamiltonian (i.e., any lattice model of finite-dimensional bosonic degrees of freedom) can arise as the low-energy description of such an Ising model. At a conceptual level, this uncovers new connections, such as how the spin-1/2 Heisenberg model and Kitaev honeycomb model arise from a four-state Potts model and a four-state loop model, respectively. We will also see how this universality of Ising models points toward new ways of realizing exotic quantum magnets using minimal ingredients in solid state and cold atom systems.