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arXiv · 2505.24130

Instantons and topological order in two-leg electron ladders: A universality class

S. -R. Eric Yang·Hyun Cheol Lee·Hoang-Anh Le·In-Hwan Lee
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Abstract

Our numerical study of the disordered Hubbard model with nearest-neighbor hopping shows that a two-leg electron ladder has a finite topological entanglement entropy in the regime where the density of states exhibits an exponentially decaying gap. The value of the topological entanglement entropy suggests that two-leg ladders belong to the same universality class as graphene zigzag nanoribbons, despite several structural differences. A Shankar-Witten-type bosonization Lagrangian with disorder captures several features of the numerically obtained results for disordered two-leg ladders. Additionally, we propose a Lagrangian in which the fusion of two semions residing on different chains generates a fermion (instanton). We apply this Lagrangian within the framework of the pinned charge-density-wave model and compute the relevant Green's function using the bosonization method. This approach predicts a linear density of states at a critical disorder strength. Below this threshold, a soft gap emerges, which is in qualitative agreement with our numerical results.

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S. -R. Eric Yang, Hyun Cheol Lee, Hoang-Anh Le, In-Hwan Lee. 2025-05-30. Instantons and topological order in two-leg electron ladders: A universality class. https://doi.org/10.1103/physrevb.111.205144

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