Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2103.16278 · Physical Review Research

Quantum dots as parafermion detectors

Raphael L. R. C. Teixeira, Luis G. G. V. Dias da Silva

Published Jul 2, 2021• 6 citations
arXivHTMLPDF

Abstract

Parafermionic zero modes, ${\mathbb{Z}}_{n}$-symmetric generalizations of the well-known ${\mathbb{Z}}_{2}$ Majorana zero modes, can emerge as edge states in topologically nontrivial strongly correlated systems displaying fractionalized excitations. In this paper, we investigate how signatures of parafermionic zero modes can be detected by its effects on the properties of a quantum dot tunnel-coupled to a system hosting such states. Concretely, we consider a strongly correlated one-dimensional fermionic model supporting ${\mathbb{Z}}_{4}$ parafermionic zero modes coupled to an interacting quantum dot at one of its ends. By using a combination of density matrix renormalization group calculations and analytical approaches, we show that the dot's zero-energy spectral function and average occupation numbers can be used to distinguish between trivial, ${\mathbb{Z}}_{4}$ and $2\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2}$ phases of the system. The present work opens the prospect of using quantum dots as detection tools to probe nontrivial topological phases in strongly correlated systems.

DOI
10.1103/physrevresearch.3.033014

Related papers

Parafermionic modes in correlated electron systems

Raphael L. R. C. Teixeira

Obtaining non-abelian anyons is one of the primary goals within the field of topological states of matter.The simplest of these anyons, Majorana bound states (MBSs) [1], have been proposed as candidates for implementing topological quantum computation relying on its non-abelian statistics [2][3][4][5].Parafermions bound states (PBSs) can be regarded as MBSs [6,7].PBS have richer non-abelian exchange statistics compared to MBS and would thus offer advantages for quantum computation.In contrast to MBS, PBS usually require strong interactions between electrons and has been proposed to exist, for instance, in fractional quantum Hall insulators with induced superconductivity [8-10].Tight-binding models have also been suggested to host PBSs [11][12][13], although in some cases they are nontopological [14].Recently, Kondo devices have also been proposed to host parafermionic states [15,16].Nonetheless, in all setups, many-body interactions are necessary for the existence of PBS.In this thesis, we are concerned with the properties of PBSs that can be used in experimental setups.While most of the work developed here concerns fermionic models [17,18], we also investigate a continuous model of fractional quantum Hall insulators with induced superconductivity [19].This work is, therefore, divided into two parts.In the first part, we examine the fermionic models using Density Matrix Renormalization Group (DMRG) [20][21][22] as well as some properties of Fock-parafermion [11].We start with a proposal on how to use Quantum dots (QDs) to probe the existence of Z 4 parafermions and differentiate it from 2 MBSs (2xZ 2 ).Then, we introduce two fermionic models that host Z 3 parafermions.We show the topological equivalence of the models and their properties.In the second part, we use a combination of analytical (semiclassical instanton approximation) and numerical (quantum Monte Carlo simulations) techniques to determine the effective parafermion Hamiltonian and its ground state splitting in a fractional quantum Hall insulators with induced superconductivity.

•Mar 21, 2023•0 citations

Dynamical topological excitations in parafermion chains

Vilja Kaskela, J. L. Lado

Parafermions are elusive fractional excitations potentially emerging in fractional quantum Hallsuperconductor junctions and represent one of the major milestones in fractional quantum matter.However, generic models of parafermions are not analytically solvable, and understanding their topological modes is a bigger challenge than conventional Majorana modes.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.

arXiv:2011.06462•Physical Review Research•Jan 29, 2021•18 citations

Edge Z3 parafermions in fermionic lattices

Raphael L. R. C. Teixeira, Luis G. G. V. Dias da Silva

Parafermion modes are non-Abelian anyons which were introduced as ${\mathbb{Z}}_{N}$ generalizations of ${\mathbb{Z}}_{2}$ Majorana states. In particular, ${\mathbb{Z}}_{3}$ parafermions can be used to produce Fibonacci anyons, laying a path towards universal topological quantum computation. Due to their fractional nature, much of the theoretical work on ${\mathbb{Z}}_{3}$ parafermions has relied on bosonization methods or parafermionic quasiparticles. In this paper, we introduce a representation of ${\mathbb{Z}}_{3}$ parafermions in terms of purely fermionic models. We establish the equivalency of a family of lattice fermionic models written in the basis of the $t\ensuremath{-}J$ model with a Kitaev-like chain supporting free ${\mathbb{Z}}_{3}$ parafermionic modes at its ends. By using density matrix renormalization group calculations, we are able to characterize the topological phase transition and study the effect of local operators (doping and magnetic fields) on the spatial localization of the parafermionic modes and their stability. Moreover, we discuss the necessary ingredients towards realizing ${\mathbb{Z}}_{3}$ parafermions in strongly interacting electronic systems.

arXiv:2111.10147•Physical review. B./Physical review. B•May 13, 2022•5 citations

Fermionized parafermions and symmetry-enriched Majorana modes

Aaron Chew, David F. Mross, Jason Alicea

Parafermion zero modes are generalizations of Majorana modes that underlie comparatively rich non-Abelian-anyon properties. We introduce exact mappings that connect parafermion chains, which can emerge in two-dimensional fractionalized media, to strictly one-dimensional fermionic systems. In particular, we show that parafermion zero modes in the former setting translate into symmetry-enriched Majorana modes that intertwine with a bulk order parameter---yielding braiding and fusion properties that are impossible in standard Majorana platforms. Fusion characteristics of symmetry-enriched Majorana modes are directly inherited from the associated parafermion setup and can be probed via two kinds of anomalous pumping cycles that we construct. Most notably, our mappings relate ${\mathbb{Z}}_{4}$ parafermions to conventional electrons with time-reversal symmetry. In this case, one of our pumping protocols entails fairly minimal experimental requirements: Cycling a weakly correlated wire between a trivial phase and time-reversal-invariant topological superconducting state produces an edge magnetization with quadrupled periodicity. Our work highlights new avenues for exploring beyond-Majorana physics in experimentally relevant one-dimensional electronic platforms, including proximitized ferromagnetic chains.

arXiv:1802.04809•Physical review. B./Physical review. B•Aug 27, 2018•41 citations

Electronic ladder model harboring Z 4 parafermions

Botond Osváth, Gergely Barcza, Örs Legeza +2 more

Parafermions are anyons with the potential for realizing nonlocal qubits that are resilient to local perturbations. Compared with Majorana zero modes, braiding of parafermions implements an extended set of topologically protected quantum gates. This, however, comes at the price that parafermionic zero modes cannot be realized in the absence of strong interactions, posing a challenge for their theoretical depiction. In this paper, we construct a simple lattice model for interacting spinful electrons with parafermionic zero-energy modes. The explicit microscopic nature of the considered model highlights realization avenues for these exotic excitations in recently fabricated quantum dot arrays. By density matrix renormalization group calculations, we identify a broad range of parameters, with well-localized zero modes, whose parafermionic nature is substantiated by their unique $8\ensuremath{\pi}$ periodic Josephson spectrum.

arXiv:2311.07359•Physical review. B./Physical review. B•Aug 23, 2024•1 citation

Modos parafermiônicos em sistemas de elétrons correlacionados

Raphael L. R. C. Teixeira

Obtaining non-abelian anyons is one of the primary goals within the field of topological states of matter. The simplest of these anyons, Majorana bound states (MBSs), have been proposed as candidates for implementing topological quantum computation relying on its non-abelian statistics. Parafermions bound states (PBSs) can be regarded as ZN generalizations of the Z2-symmetric MBSs. PBS have richer non-abelian exchange statistics compared to MBS and would thus offer advantages for quantum computation. In contrast to MBS, PBS usually require strong interactions between electrons and has been proposed to exist, for instance, in fractional quantum Hall insulators with induced superconductivity. Tight-binding models have also been suggested to host PBSs, although in some cases they are nontopological. Recently, Kondo devices have also been proposed to host parafermionic states. Nonetheless, in all setups, many-body interactions are necessary for the existence of PBS. In this thesis, we are concerned with the properties of PBSs that can be used in experimental setups. While most of the work developed here concerns fermionic models, we also investigate a continuous model of fractional quantum Hall insulators with induced superconductivity. This work is, therefore, divided into two parts. In the first part, we examine the fermionic models using Density Matrix Renormalization Group (DMRG) as well as some properties of Fock-parafermion. We start with a proposal on how to use Quantum dots (QDs) to probe the existence of Z4 parafermions and differentiate it from 2 MBSs (2xZ2). Then, we introduce two fermionic models that host Z3 parafermions. We show the topological equivalence of the models and their properties. In the second part, we use a combination of analytical (semiclassical instanton approximation) and numerical (quantum Monte Carlo simulations) techniques to determine the effective parafermion Hamiltonian and its ground state splitting in a fractional quantum Hall insulators with induced superconductivity.

•Mar 21, 2023•0 citations
Parafermionic zero modes, Zn{\mathbb{Z}}_{n}Zn​-symmetric generalizations of the well-known Z2{\mathbb{Z}}_{2}Z2​ Majorana zero modes, can emerge as edge states in topologically nontrivial strongly correlated systems displaying fractionalized excitations. In this paper, we investigate how signatures of parafermionic zero modes can be detected by its effects on the properties of a quantum dot tunnel-coupled to a system hosting such states. Concretely, we consider a strongly correlated one-dimensional fermionic model supporting Z4{\mathbb{Z}}_{4}Z4​ parafermionic zero modes coupled to an interacting quantum dot at one of its ends. By using a combination of density matrix renormalization group calculations and analytical approaches, we show that the dot's zero-energy spectral function and average occupation numbers can be used to distinguish between trivial, Z4{\mathbb{Z}}_{4}Z4​ and 2\ifmmode×\else\texttimes\fiZ22\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2}2\ifmmode×\else\texttimes\fiZ2​ phases of the system. The present work opens the prospect of using quantum dots as detection tools to probe nontrivial topological phases in strongly correlated systems.
Obtaining non-abelian anyons is one of the primary goals within the field of topological states of matter.The simplest of these anyons, Majorana bound states (MBSs) [1], have been proposed as candidates for implementing topological quantum computation relying on its non-abelian statistics [2][3][4][5].Parafermions bound states (PBSs) can be regarded as MBSs [6,7].PBS have richer non-abelian exchange statistics compared to MBS and would thus offer advantages for quantum computation.In contrast to MBS, PBS usually require strong interactions between electrons and has been proposed to exist, for instance, in fractional quantum Hall insulators with induced superconductivity [8-10].Tight-binding models have also been suggested to host PBSs [11][12][13], although in some cases they are nontopological [14].Recently, Kondo devices have also been proposed to host parafermionic states [15,16].Nonetheless, in all setups, many-body interactions are necessary for the existence of PBS.In this thesis, we are concerned with the properties of PBSs that can be used in experimental setups.While most of the work developed here concerns fermionic models [17,18], we also investigate a continuous model of fractional quantum Hall insulators with induced superconductivity [19].This work is, therefore, divided into two parts.In the first part, we examine the fermionic models using Density Matrix Renormalization Group (DMRG) [20][21][22] as well as some properties of Fock-parafermion [11].We start with a proposal on how to use Quantum dots (QDs) to probe the existence of Z 4 parafermions and differentiate it from 2 MBSs (2xZ 2 ).Then, we introduce two fermionic models that host Z 3 parafermions.We show the topological equivalence of the models and their properties.In the second part, we use a combination of analytical (semiclassical instanton approximation) and numerical (quantum Monte Carlo simulations) techniques to determine the effective parafermion Hamiltonian and its ground state splitting in a fractional quantum Hall insulators with induced superconductivity.
Parafermions are elusive fractional excitations potentially emerging in fractional quantum Hallsuperconductor junctions and represent one of the major milestones in fractional quantum matter.However, generic models of parafermions are not analytically solvable, and understanding their topological modes is a bigger challenge than conventional Majorana modes.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.
Parafermion modes are non-Abelian anyons which were introduced as ZN{\mathbb{Z}}_{N}ZN​ generalizations of Z2{\mathbb{Z}}_{2}Z2​ Majorana states. In particular, Z3{\mathbb{Z}}_{3}Z3​ parafermions can be used to produce Fibonacci anyons, laying a path towards universal topological quantum computation. Due to their fractional nature, much of the theoretical work on Z3{\mathbb{Z}}_{3}Z3​ parafermions has relied on bosonization methods or parafermionic quasiparticles. In this paper, we introduce a representation of Z3{\mathbb{Z}}_{3}Z3​ parafermions in terms of purely fermionic models. We establish the equivalency of a family of lattice fermionic models written in the basis of the $t\ensuremath{-}J$ model with a Kitaev-like chain supporting free Z3{\mathbb{Z}}_{3}Z3​ parafermionic modes at its ends. By using density matrix renormalization group calculations, we are able to characterize the topological phase transition and study the effect of local operators (doping and magnetic fields) on the spatial localization of the parafermionic modes and their stability. Moreover, we discuss the necessary ingredients towards realizing Z3{\mathbb{Z}}_{3}Z3​ parafermions in strongly interacting electronic systems.
Parafermion zero modes are generalizations of Majorana modes that underlie comparatively rich non-Abelian-anyon properties. We introduce exact mappings that connect parafermion chains, which can emerge in two-dimensional fractionalized media, to strictly one-dimensional fermionic systems. In particular, we show that parafermion zero modes in the former setting translate into symmetry-enriched Majorana modes that intertwine with a bulk order parameter---yielding braiding and fusion properties that are impossible in standard Majorana platforms. Fusion characteristics of symmetry-enriched Majorana modes are directly inherited from the associated parafermion setup and can be probed via two kinds of anomalous pumping cycles that we construct. Most notably, our mappings relate Z4{\mathbb{Z}}_{4}Z4​ parafermions to conventional electrons with time-reversal symmetry. In this case, one of our pumping protocols entails fairly minimal experimental requirements: Cycling a weakly correlated wire between a trivial phase and time-reversal-invariant topological superconducting state produces an edge magnetization with quadrupled periodicity. Our work highlights new avenues for exploring beyond-Majorana physics in experimentally relevant one-dimensional electronic platforms, including proximitized ferromagnetic chains.
Parafermions are anyons with the potential for realizing nonlocal qubits that are resilient to local perturbations. Compared with Majorana zero modes, braiding of parafermions implements an extended set of topologically protected quantum gates. This, however, comes at the price that parafermionic zero modes cannot be realized in the absence of strong interactions, posing a challenge for their theoretical depiction. In this paper, we construct a simple lattice model for interacting spinful electrons with parafermionic zero-energy modes. The explicit microscopic nature of the considered model highlights realization avenues for these exotic excitations in recently fabricated quantum dot arrays. By density matrix renormalization group calculations, we identify a broad range of parameters, with well-localized zero modes, whose parafermionic nature is substantiated by their unique $8\ensuremath{\pi}$ periodic Josephson spectrum.
Obtaining non-abelian anyons is one of the primary goals within the field of topological states of matter. The simplest of these anyons, Majorana bound states (MBSs), have been proposed as candidates for implementing topological quantum computation relying on its non-abelian statistics. Parafermions bound states (PBSs) can be regarded as ZN generalizations of the Z2-symmetric MBSs. PBS have richer non-abelian exchange statistics compared to MBS and would thus offer advantages for quantum computation. In contrast to MBS, PBS usually require strong interactions between electrons and has been proposed to exist, for instance, in fractional quantum Hall insulators with induced superconductivity. Tight-binding models have also been suggested to host PBSs, although in some cases they are nontopological. Recently, Kondo devices have also been proposed to host parafermionic states. Nonetheless, in all setups, many-body interactions are necessary for the existence of PBS. In this thesis, we are concerned with the properties of PBSs that can be used in experimental setups. While most of the work developed here concerns fermionic models, we also investigate a continuous model of fractional quantum Hall insulators with induced superconductivity. This work is, therefore, divided into two parts. In the first part, we examine the fermionic models using Density Matrix Renormalization Group (DMRG) as well as some properties of Fock-parafermion. We start with a proposal on how to use Quantum dots (QDs) to probe the existence of Z4 parafermions and differentiate it from 2 MBSs (2xZ2). Then, we introduce two fermionic models that host Z3 parafermions. We show the topological equivalence of the models and their properties. In the second part, we use a combination of analytical (semiclassical instanton approximation) and numerical (quantum Monte Carlo simulations) techniques to determine the effective parafermion Hamiltonian and its ground state splitting in a fractional quantum Hall insulators with induced superconductivity.