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Abstract

Topological phases are characterised by a robustness against perturbations, yet it is instructive to examine how sufficiently strong perturbations can ultimately destroy them. Here, we discuss two representative examples.

First, we study the breakdown of the quantised Hall conductance in the non-interacting Haldane model under disorder and in the presence of a trivial mass term. We find that mass-driven quantum Hall plateau transitions exhibit critical behaviour that is distinct from purely disorder-driven transitions, including continuously varying critical exponents.

Second, motivated by recent evidence for time-reversal symmetry breaking fractional Chern insulators in twisted MoTe2 bilayers, we reexamine the stability of time-reversal invariant fractional topological insulators. Focusing on a model of two interacting fermionic species occupying a time-reversal invariant pair of flat Hofstadter bands with opposite magnetic fields, we map out the ground-state phase diagram using density-matrix renormalisation group methods.

We confirm the stability of the ν=1/3+1/3 fractional topological insulator against inter-species interactions and identify a transition to a topologically trivial phase when inter- and intra-species interactions become comparable. We propose the helical entanglement spectrum as a diagnostic of this phase and show that it reproduces the edge-mode counting of a U(1)×U(1) chiral boson theory.

Finally, we comment on recent progress toward connecting such theoretical diagnostics to experimentally accessible probes. In particular, we highlight work demonstrating that quantum state tomography can, in principle, be reconstructed from neutron scattering correlation functions in quantum spin systems. While not yet directly applicable to itinerant carriers, this establishes a concrete route toward experimentally accessing entanglement- and topology-based diagnostics.