Abstract:
Hilbert space, the mathematical representation of possible states of a quantum system, is a vast place when the system is a macroscopic piece of matter. The traditional theory of symmetry breaking reduces this overwhelming amount of information to three key quantities: the energy (or Hamiltonian), the symmetry of the energy, and the pattern of symmetry breaking; however, the existence of exotic phases of matter like the fractional quantum hall effect demonstrates the need for a more general theory. This theory must take into account entanglement, or the the non-trivial quantum correlations between sub-regions of a larger quantum system. Here I show how the pattern of entanglement in a many body system can be visualized using higher dimensional geometry and how this picture connects two new tools in many body physics: entanglement renormalization and holographic gauge/gravity duality.