Absence of gapless Majorana edge modes in few-leg bosonic flux ladders

Abstract

The search for Majorana excitations has seen tremendous efforts in recent years, ultimately aiming for their individual controllability in future topological quantum computers. A promising framework to realize such exotic Majorana fermions are topologically ordered non-Abelian phases of matter, such as certain fractional quantum Hall states. Quantum simulators provide unprecedented controllability and versatility to investigate such states, and developing experimentally feasible schemes to realize and identify them is of immediate relevance. Motivated by recent experiments, we consider bosons on coupled chains, subjected to a magnetic flux and experiencing Hubbard repulsion. At magnetic filling factor $\nu =1$, similar systems on cylinders have been found to host the non-Abelian Moore-Read Pfaffian state in the bulk. Here, we address the question whether more realistic few-leg ladders can host this exotic state and its chiral Majorana edge states. To this end, we perform extensive DMRG simulations and determine the central charge of the ground state. While we do not find any evidence of gapless Majorana edge modes in systems of up to six legs, exact diagonalization of small systems reveals evidence for the Pfaffian state in the entanglement structure. By systematically varying the number of legs and monitoring the appearance and disappearance of this signal, our work highlights the importance of finite-size effects for the realization of exotic states in experimentally realistic systems.

References in corpus (23)

• The density-matrix renormalization group in the age of matrix product states
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Fractional Quantum Hall Effect in Optical Lattices
• An Aharonov-Bohm interferometer for determining Bloch band topology
• Atomic three-body loss as a dynamical three-body interaction
• A Strictly Single-Site DMRG Algorithm with Subspace Expansion
• Realization of a fractional quantum Hall state with ultracold atoms
• Detecting Chiral Edge States in the Hofstadter Optical Lattice
• Vortex and Meissner phases of strongly-interacting bosons on a two-leg ladder
• Exploring Large-Scale Entanglement in Quantum Simulation
• Symmetry-broken states in a system of interacting bosons on a two-leg ladder with a uniform Abelian gauge field
• Engineering and probing non-Abelian chiral spin liquids using periodically driven ultracold atoms
• Realization of fractional quantum Hall state with interacting photons
• Fractional Chern insulators of few bosons in a box: Hall plateaus from center-of-mass drifts and density profiles
• Particle Entanglement Spectra for Quantum Hall states on Lattices
• Quantum simulation of three-body interactions in weakly driven quantum systems
• Fluctuations and Entanglement spectrum in quantum Hall states
• Bosonic Pfaffian State in the Hofstadter-Bose-Hubbard Model
• Characterizing fractional topological phases of lattice bosons near the first Mott lobe
• Snapshot-based detection of $\frac{1}{2}$-Laughlin states: coupled chains and central charge
• Growing Extended Laughlin States in a Quantum Gas Microscope: A Patchwork Construction
• Bayesian Optimization for Robust State Preparation in Quantum Many-Body Systems
• Adiabatic preparation of fractional Chern insulators from an effective thin-torus limit

Cited by in corpus (1)

• Realization of strongly-interacting Meissner phases in large bosonic flux ladders