Instantons and topological order in two-leg electron ladders: A universality class
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.
Keywords
Cite
@article{arxiv.2505.24130,
title = {Instantons and topological order in two-leg electron ladders: A universality class},
author = {S. -R. Eric Yang and Hyun Cheol Lee and Hoang-Anh Le and In-Hwan Lee},
journal= {arXiv preprint arXiv:2505.24130},
year = {2025}
}