Kavli Affiliate: Shenghan Jiang
| First 5 Authors: Chao Xu, Yixin Ma, Shenghan Jiang, ,
| Summary:
The study of topological band insulators has revealed fascinating phases
characterized by band topology indices, harboring extraordinary boundary modes
protected by anomalous symmetry actions. In strongly correlated systems, where
the traditional notion of electronic bands becomes obsolete, it has been
established that topological insulator phases persist as stable phases,
separate from trivial insulators. However, due to the inability to express the
ground states of such systems as Slater determinants, the formulation of
generic variational wavefunctions for numerical simulations is highly
desirable. In this paper, we tackle this challenge by developing a
comprehensive framework for fermionic tensor network states. Starting from
simple assumptions, we obtain possible sets of tensor equations for any given
symmetry group, capturing consistent relations governing symmetry
transformation rules on tensor legs. We then examine the connections between
these tensor equations and topological insulators by construing edge theories
and extracting quantum anomaly data from each set of tensor equations. By
exhaustively exploring all possible sets of equations, we achieve a systematic
classification of topological insulator phases. Imposing the solutions of a
given set of equations onto local tensors, we obtain generic variational
wavefunctions for corresponding topological insulator phases. Our methodology
provides a crucial first step towards simulating topological insulators in
strongly correlated systems. We discuss the limitations and potential
generalizations of our results, paving the way for further advancements in this
field.
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