Condensed Matter Theory

Abstract:

We consider the optical conductivity σ1(ω) in the metallic phase of the one-dimensional Hubbard model. Our results focus on the vicinity of half filling and the frequency regime around the optical gap in the Mott insulating phase. By means of a density-matrix renormalization group implementation of the correction-vector approach, σ1(ω) is computed for a range of interaction strengths and dopings. We identify an energy scale Eopt above which the optical conductivity shows a rapid increase. We then use a mobile impurity model in combination with exact results to determine the behavior of σ1(ω) for frequencies just above Eopt which is in agreement with our numerical data. As a main result, we find that this onset behavior is not described by a power law.

Abstract:

We concisely review the recent evolution in the study of parafermions—exotic emergent excitations that generalize Majorana fermions and similarly underpin a host of novel phenomena. First we generalize the intimate connection between the -symmetric Ising quantum spin chain and Majorana fermions to -symmetric chains and parafermions. In particular, we highlight how parafermion chains host a topological phase featuring protected edge zero modes. We then tour several blueprints for the laboratory realization of parafermion zero modes—focusing on quantum Hall/superconductor hybrids, quantum Hall bilayers, and two-dimensional topological insulators—and describe striking experimental fingerprints that they provide. Finally, we discuss how coupled parafermion arrays in quantum Hall architectures yield topological phases that potentially furnish hardware for a universal, intrinsically decoherence-free quantum computer.