Speaker
Description
Topologically ordered phases in two-dimensional gapped quantum systems provide a fundamental example of quantum phases that cannot be understood within the conventional framework of symmetry breaking. Their universal properties are widely believed to be described by topological quantum field theories (TQFTs). However, establishing this description directly from the microscopic properties of quantum many-body states remains a challenging problem. In this talk, I will discuss an information-theoretic approach to this problem based on the entanglement bootstrap. The basic idea is to characterize a gapped quantum state through universal constraints on its local reduced density matrices, motivated by the area law of entanglement. Remarkably, these local entropic constraints are already sufficient to derive nontrivial global structures associated with topological order. In particular, one can identify superselection sectors and derive the fusion rules of anyonic excitations without assuming an underlying TQFT or microscopic quasiparticle description.
I will explain the basic framework and illustrate how topological data emerge from purely quantum-information-theoretic properties of the ground state. I will also discuss what is currently known about the scope and limitations of this approach, including the issue of spurious topological entanglement entropy. Finally, I will briefly discuss ongoing work toward connecting the entanglement-bootstrap framework with operator-algebraic approaches to infinite quantum systems, with the aim of developing a unified formulation of topological order in the thermodynamic limit.