Localized Majorana-like modes in a number conserving setting: An exactly solvable model

TL;DR

This paper introduces a number conserving fermionic model supporting Majorana-like edge states, characterized by an exactly solvable line and numerical analysis revealing topological properties, edge correlations, and a gapped spectrum despite a gapless Hamiltonian.

Contribution

It presents an exactly solvable model with Majorana-like modes in a number conserving setting, expanding understanding of topological phases in interacting fermion systems.

Findings

Presence of Majorana-like edge modes in a number conserving model

Topologically non-trivial ground state wave-function

Existence of a gap in the single particle spectrum despite a gapless Hamiltonian

Abstract

In this letter we present, in a number conserving framework, a model of interacting fermions in a two-wire geometry supporting non-local zero-energy Majorana-like edge excitations. The model has an exactly solvable line, on varying the density of fermions, described by a topologically non-trivial ground state wave-function. Away from the exactly solvable line we study the system by means of the numerical density matrix renormalization group. We characterize its topological properties through the explicit calculation of a degenerate entanglement spectrum and of the braiding operators which are exponentially localized at the edges. Furthermore, we establish the presence of a gap in its single particle spectrum while the Hamiltonian is gapless, and compute the correlations between the edge modes as well as the superfluid correlations. The topological phase covers a sizeable portion of the phase diagram, the solvable line being one of its boundaries.