Interpretation of thermal conductance of the ν = 5/2 edge
Physical Review B American Physical Society 97:12 (2018) 121406(R)
Abstract:
Recent experiments [Banerjee et al, arXiv:1710.00492] have measured thermal conductance of the ν = 5/2 edge in a GaAs electron gas and found it to be quantized as K ≈ 5/2 (in appropriate dimensionless units). This result is unexpected, as prior numerical work predicts that the ν = 5/2 state should be the Anti-Pfaffian phase of matter, which should have quantized K = 3/2. The purpose of this paper is to propose a possible solution to this conflict: if the Majorana edge mode of the Anti-Pfaffian does not thermally equilibrate with the other edge modes, then K = 5/2 is expected. I briefly discuss a possible reason for this nonequilibration, and what should be examined further to determine if this is the case.Excitations in the higher lattice gauge theory model for topological phases III: the 3+1d case
Physical Review B American Physical Society 109:3 (2024) 035152
Abstract:
In this, the third paper in our series describing the excitations of the higher lattice gauge theory model for topological phases, we will examine the 3+1d case in detail. We will explicitly construct the ribbon and membrane operators which create the topological excitations, and use these creation operators to find the pattern of condensation and confinement. We also use these operators to find the braiding relations of the excitations, and to construct charge measurement operators which project to states of definite topological charge.Topological and nontopological degeneracies in generalized string-net models
Physical Review B American Physical Society 109 (2024) 045130
Abstract:
Generalized string-net models have been proposed recently in order to enlarge the set of possible topological quantum phases emerging from the original string-net construction. In the present work we do not consider vertex excitations, and we restrict ourselves to plaquette excitations, or fluxons, that satisfy important identities. We explain how to compute the energy-level degeneracies of the generalized string-net Hamiltonian associated with an arbitrary unitary fusion category. In contrast to the degeneracy of the ground state, which is purely topological, the degeneracy of excited energy levels depends not only on the Drinfeld center of the category, but also on internal multiplicities obtained from the tube algebra defined from the category. For a noncommutative category, these internal multiplicities result in extra nontopological degeneracies. Our results are valid for any trivalent graph and any orientable surface. We illustrate our findings with nontrivial examples.Comment on “Anomalous reentrant 5/2 quantum Hall phase at moderate Landau-level-mixing strength”
Physical Review Letters American Physical Society 132:2 (2024) 029601
Comment on “Anomalous Reentrant 5/2 Quantum Hall Phase at Moderate Landau-Level-Mixing Strength”
Physical Review Letters (2024)