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Interacting topological quantum chemistry in 2D with many-body real space invariants
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Interacting topological quantum chemistry in 2D with many-body real space invariants
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Journal Article
Interacting topological quantum chemistry in 2D with many-body real space invariants
2024
Overview
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
U
(1) particle number, they yield many-body fragile topological indices, which we use to identify which single-particle fragile states are many-body topological or trivial at weak coupling. To this end, we construct an exactly solvable Hamiltonian with single-particle fragile topology that is adiabatically connected to a trivial state through strong coupling. We then define global many-body RSIs on periodic boundary conditions. They reduce to Chern numbers in the band theory limit, but also identify strongly correlated stable topological phases with no single-particle counterpart. Finally, we show that the many-body local RSIs appear as quantized coefficients of Wen-Zee terms in the topological quantum field theory describing the phase.
While the classification of single-particle topological phases has been established, recent efforts have been made to extend it to interacting limit. Here the authors present a classification of interacting topological systems in 2D based on the generalization of real space invariants.
