Abstract: In [1] we constructed a family of two-dimensional topological stabilizer codes on continuous variable (CV) degrees of freedom, which generalize homological rotor codes and the toric-GKP code. Our topological codes are built using the concept of boson condensation -- we start from a parent stabilizer code based on an R gauge theory and condense various bosonic excitations. This produces a large class of topological CV stabilizer codes, including ones that are characterized by the anyon theories of U(1)2n×U(1)−2m Chern-Simons theories, for arbitrary pairs of positive integers (n,m). Most notably, this includes anyon theories that are non-chiral and nevertheless do not admit a gapped boundary. It is widely believed that such anyon theories cannot be realized by any stabilizer model on finite-dimensional systems. We conjecture that these CV codes go beyond codes obtained from concatenating a topological qudit code with a local encoding into CVs, and thus, constitute the first example of topological codes that are intrinsic to CV systems.
In this talk I want to show the construction and give some background on how to understand the anyon theories realized by these model.
The codes also give rise to topologically ordered Hamiltonians which we also study in [1]. We show that, although they have a gapless spectrum, they can become gapped with the addition of a quadratic perturbation. We show that similar methods can be used to construct a gapped Hamiltonian whose anyon theory agrees with a U(1)_2 Chern-Simons theory. I my talk I want to sketch the construction and highlight connection to a particular factorization of the operator algebra and related open questions.
[1]: arXiv 2411.04993
*We strongly encourage attendees to use their full name (and if possible, their UMD credentials) to join the zoom session.*