Quantum information, fractional quantum Hall effect and other quantum matter problems
Quantum information theory has provided invaluable insights for quantum many-body systems. One of the fundamental tools in this arsenal is the entanglement entropy. B. Estienne developed a new method (cyclic orbifolds from CFT) to compute the Nth Rényi entanglement entropies of critical one-dimensional quantum many-body systems, an approach also applicable to a variety of situations, such as non-unitary CFTs, multiple intervals, finite temperature and finite size, and/or entropy in an excited state. In collaboration with L. Charles (Institut de Mathématiques, Jussieu) Estienne established the validity of the Area Law for the the leading behavior of the entanglement entropy of the integer Quantum Hall Effect, for arbitrary geometries and space dimensions. The group also studied symmetry-resolved entropies (computed for each symmetry sector of the Hilbert space) in 1d systems (gapped or critical) and 2d systems (graphene, FQHE). Strikingly, the entanglement entropy tends to be equally distributed in all symmetry sectors, following a kind of equipartition.
In the fractional quantum Hall effect (FQHE) 2d electrons subjected to a strong magnetic field form a collective state with fractionalized charge and statistics and display distinctive topological characteristics. It arises in various materials, including graphene and gallium arsenide, and has potential applications in quantum computing and information processing. Estienne´s research focuses on different aspects of FQHE wavefunctions, from their development using CFT to their numerical implementation using Matrix Product States. The latter has enabled them to reliably extract correlation lengths, anyon statistics, and topological entanglement entropy for numerous model wavefunctions.
Estienne studied the fluctuations of an observable in a (large) portion of a periodically driven quantum sample, and showed that there exists a large, and experimentally relevant, set of states and observables that share the same universal shape dependence for their fluctuations. He also characterised the dependence of the corrections on local geometric quantities.
