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 and anomalous boundary modes protected
by global symmetries. In strongly correlated systems, where the traditional
notion of electronic bands becomes obsolete, it has been established that the
topological insulator phases persist as stable phases, separate from the
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 for two-dimensional topological
insulators 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 non-chiral 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 non-chiral 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 an important 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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