Entanglement Spectroscopy and probing the Li-Haldane Conjecture in Topological Quantum Matter
1Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck 6020, Austria
2Center for Quantum Physics, University of Innsbruck, Innsbruck 6020, Austria
3JILA, Department of Physics, University of Colorado, Boulder CO 80309, USA
Published: | 2022-04-27, volume 6, page 702 |
Eprint: | arXiv:2110.03913v2 |
Doi: | https://doi.org/10.22331/q-2022-04-27-702 |
Citation: | Quantum 6, 702 (2022). |
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Abstract
Topological phases are characterized by their entanglement properties, which is manifest in a direct relation between entanglement spectra and edge states discovered by Li and Haldane. We propose to leverage the power of synthetic quantum systems for measuring entanglement via the Entanglement Hamiltonian to probe this relationship experimentally. This is made possible by exploiting the quasi-local structure of Entanglement Hamiltonians. The feasibility of this proposal is illustrated for two paradigmatic examples realizable with current technology, an integer quantum Hall state of non-interacting fermions on a 2D lattice and a symmetry protected topological state of interacting fermions on a 1D chain. Our results pave the road towards an experimental identification of topological order in strongly correlated quantum many-body systems.

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