Abstract
Topological excitations in many-body systems are one of the paradigmatic cornerstones of modern condensed matter physics. In particular, parafermions are elusive fractional excitations potentially emerging in fractional quantum Hall-superconductor junctions, and represent one of the major milestones in fractional quantum matter. Here, by using a combination of tensor network and kernel polynomial techniques, we demonstrate the emergence of zero modes and finite energy excitations in many-body parafermion chains. We show the appearance of zero energy modes in the many-body spectral function at the edge of a topological parafermion chain, their relation with the topological degeneracy of the system, and we compare their physics with the Majorana bound states of topological superconductors. We demonstrate the robustness of parafermion topological modes with respect to a variety of perturbations, and we show how weakly coupled parafermion chains give rise to in-gap excitations. Our results exemplify the versatility of tensor network methods for studying dynamical excitations of interacting parafermion chains, and highlight the robustness of topological modes in parafermion models.
Highlights
Unconventional excitations in quantum materials are a central research area in modern condensed matter physics [1,2]
We show the appearance of zero-energy modes in the many-body spectral function at the edge of a topological parafermion chain, their relation with the topological degeneracy of the system, and we compare their physics with the Majorana bound states of topological superconductors
Generic parafermion models are challenging to study analytically, and their topological excitations are less understood than those of single-particle topological systems. To study this interacting model, we employed a combination of tensor network and kernel polynomial techniques that allow addressing the full excitation spectra of the interacting Hamiltonian
Summary
Unconventional excitations in quantum materials are a central research area in modern condensed matter physics [1,2]. The emergence of Majorana zero modes [7,8] in these systems puts forward the possibility of using superconductors as a noise-resilient platform for topological quantum computing [9,10,11]. Parafermions realize quantum excitations with generalized commutation relations, providing a powerful platform for topological quantum computing, overcoming a limitation of Majorana bound states [9,10,23]. Majorana bound states can be described in an effectively single-particle picture with the Bogoliuvov-de-Gennes formalism The robustness of these modes to perturbations stems from their topological origin, which is associated to the existence of a single-particle nontrivial topological invariants.
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