Entanglement phases as holographic duals of anyon condensates

Topological phases are exotic states of matters which do not order locally yet exhibit a global ordering in their entanglement, making their characterization a challenging task. In this work, the authors construct an explicit holographic duality between topological phases in the bulk and the structure of the entanglement spectrum at its boundary, thereby establishing a one-to-one correspondence between different bulk topological orders and symmetry-breaking and symmetry-protected orderings of the entanglement. This allows classification and detection of topological phases holographically through ``entanglement spectroscopy'' at the boundary, and construction of order parameters that measure the condensation and confinement of anyons, and thus permits characterization of the nature of topological phase transitions.