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

TL;DR

This paper investigates the topological properties of disordered two-leg electron ladders, revealing their universality class similarity to graphene nanoribbons and identifying a phase transition characterized by a soft gap and linear density of states.

Contribution

It introduces a bosonization Lagrangian capturing disorder effects and proposes a novel fusion mechanism of semions generating fermions, advancing understanding of topological phases in disordered ladders.

Findings

Finite topological entanglement entropy in disordered ladders

Universality class matches graphene zigzag nanoribbons

Prediction of a soft gap and linear density of states at critical disorder

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.