2015
DOI: 10.1103/physrevb.92.035154
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Phase diagram of theZ3parafermionic chain with chiral interactions

Abstract: Parafermions are exotic quasiparticles with non-Abelian fractional statistics that can be realized and stabilized in 1-dimensional models that are generalizations of the Kitaev p-wave wire. We study the simplest generalization, i.e. the Z3 parafermionic chain. Using a Jordan-Wigner transform we focus on the equivalent three-state chiral clock model, and study its rich phase diagram using the density matrix renormalization group technique. We perform our analyses using quantum entanglement diagnostics which all… Show more

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Cited by 75 publications
(123 citation statements)
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“…After the experimental clarification that two zero-energy Majorana modes can be localized at the edges of a one-dimensional fermionic wire [6,7], the possibility of localizing parafermionic modes, and letting them interact, is currently under deep investigation. These excitations cannot appear in strictly one-dimensional spinless fermionic systems [8,9], but may emerge at the edge of a two-dimensional fractional topological insulator coupled to alternating ferromagnetic and superconducting materials [5,[10][11][12][13][14][15], as well as in other nanostructures or models [16][17][18][19][20][21][22][23][24].In these setups, one-dimensional chains of interacting parafermions arise, which, in certain circumstances, display TO and edge Z N parafermionic modes [5,[25][26][27][28][29][30][31][32][33][34]. Such edge modes are called strong when they commute with the Hamiltonian [35] and thereby generate a N -fold degeneracy in the entire spectrum, and weak when the commutation property and associated degeneracy are restricted to the ground state manifold.…”
mentioning
confidence: 99%
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“…After the experimental clarification that two zero-energy Majorana modes can be localized at the edges of a one-dimensional fermionic wire [6,7], the possibility of localizing parafermionic modes, and letting them interact, is currently under deep investigation. These excitations cannot appear in strictly one-dimensional spinless fermionic systems [8,9], but may emerge at the edge of a two-dimensional fractional topological insulator coupled to alternating ferromagnetic and superconducting materials [5,[10][11][12][13][14][15], as well as in other nanostructures or models [16][17][18][19][20][21][22][23][24].In these setups, one-dimensional chains of interacting parafermions arise, which, in certain circumstances, display TO and edge Z N parafermionic modes [5,[25][26][27][28][29][30][31][32][33][34]. Such edge modes are called strong when they commute with the Hamiltonian [35] and thereby generate a N -fold degeneracy in the entire spectrum, and weak when the commutation property and associated degeneracy are restricted to the ground state manifold.…”
mentioning
confidence: 99%
“…In these setups, one-dimensional chains of interacting parafermions arise, which, in certain circumstances, display TO and edge Z N parafermionic modes [5,[25][26][27][28][29][30][31][32][33][34]. Such edge modes are called strong when they commute with the Hamiltonian [35] and thereby generate a N -fold degeneracy in the entire spectrum, and weak when the commutation property and associated degeneracy are restricted to the ground state manifold.…”
mentioning
confidence: 99%
“…The most robust degeneracies occur at arg(J) = π 6 (mod π 3 ) [14,15]. These degeneracies disappear for | h J | > 1 [14,19]. The clock-model can equivalently be described [24,25] in a language where the local variables are parafermions χ and ψ, which are related to the above clock variables through a Jordan-Wigner transformation [26] …”
Section: Static Systemmentioning
confidence: 99%
“…of the parafermion field characterizes the exchange (Eqs. (15), (16), and (17)) and exclusion (Eq. (18)) statistics of these degrees of freedom.…”
Section: Protection Of the Edge Modes Of The Parafermion Chain Bmentioning
confidence: 99%
“…With parafermions the idea 11,12 is to modify mesoscopically the edge of a fractional quantum spin Hall insulator by placing alternating s-wave superconducting and ferromagnetic islands in order to obtain, at low energies, an effective 1d lattice system of hybridized parafermion zero-energy modes. This basic mesoscopic blueprint has excited theoretical interest in various types of parafermion chains, with varying degrees of exoticism in their quantum phase diagrams [13][14][15][16] and also varying potential for mesoscopic realization.…”
mentioning
confidence: 99%