The topological phases of non-interacting fermions have been classified by their symmetries, culminating in a modern electronic band theory where wavefunction topology can be obtained from momentum space. Recently, Real Space Invariants (RSIs) have provided a spatially local description of the global momentum space indices. The present work generalizes this real space classification to interacting 2D states. We construct many-body local RSIs as the quantum numbers of a set of symmetry operators on open boundaries, but which are independent of the choice of boundary. Using the
Chern numbers characterize topological phases in a wide array of physical systems. However, the resilience of system topology to external perturbations makes it challenging experimentally to investigate transitions between different phases. In this study, we demonstrate the transitions of a Chern number from 0 to 3, synthesized in an electronic-nuclear spin system associated with the nitrogen-vacancy (NV) centre in diamond. The Chern number is characterized by the number of degeneracies enclosed in a control Hamiltonian parameter sphere. Topological transitions between different phases are realized by varying the radius and offset of the sphere such that the Chern number changes. We show that the measured topological phase diagram is consistent with numerical calculations and can also be mapped onto an interacting three-qubit system. The NV system may also allow access to even higher Chern numbers, which could be applied to exploring exotic topology or topological quantum information.
more » « less- PAR ID:
- 10430133
- Publisher / Repository:
- Nature Publishing Group
- Date Published:
- Journal Name:
- npj Quantum Information
- Volume:
- 9
- Issue:
- 1
- ISSN:
- 2056-6387
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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