Fock Parafermions and Self-Dual Representations of the Braid Group

@article{Cobanera2014FockPA,
  title={Fock Parafermions and Self-Dual Representations of the Braid Group},
  author={Emilio Cobanera and Gerardo Guzman Ortiz},
  journal={Physical Review A},
  year={2014},
  volume={89},
  pages={012328}
}
We introduce and describe in second quantization a family of particle species with \(p=2,3,\dots\) exclusion and \(\theta=2\pi/p\) exchange statistics. We call these anyons Fock parafermions, because they are the particles naturally associated to the parafermionic zero-energy modes, potentially realizable in mesoscopic arrays of fractional topological insulators. Their second-quantization description entails the concept of Fock algebra, i.e., a Fock space endowed with a statistical… Expand
Anyonic tight-binding models of parafermions and of fractionalized fermions
Parafermions are emergent quasi-particles which generalize Majorana fermions and possess intriguing anyonic properties. The theoretical investigation of effective models hosting them is gainingExpand
Modeling electron fractionalization with unconventional Fock spaces.
  • E. Cobanera
  • Physics, Medicine
  • Journal of physics. Condensed matter : an Institute of Physics journal
  • 2017
TLDR
Numerically the hybridization of Majorana and parafermion zero-energy edge modes caused by fractionalizing but charge-conserving tunneling is investigated. Expand
ℤ3 parafermionic chain emerging from Yang-Baxter equation
  • L. Yu, M. Ge
  • Physics, Medicine
  • Scientific reports
  • 2016
TLDR
It is shown that the parafermionic chain possesses both triple degenerate ground states and non-trivial topological winding number and is a direct generalization of 1D Kitaev model, which can be obtained from Yang-Baxter equation. Expand
A parafermionic generalization of the Jaynes–Cummings model
We introduce a parafermionic version of the Jaynes–Cummings Hamiltonian, by coupling k Fock parafermions (nilpotent of order F) to a 1D harmonic oscillator, representing the interaction with a singleExpand
Nontopological parafermions in a one-dimensional fermionic model with even multiplet pairing
We discuss a one-dimensional fermionic model with a generalized ZN even multiplet pairing extending Kitaev Z2 chain. The system shares many features with models believed to host localized edgeExpand
Superconducting Analogue of the Parafermion Fractional Quantum Hall States
Read and Rezayi $Z_k$ parafermion wavefunctions describe $\nu=2+\frac{k}{kM+2}$ fractional quantum Hall (FQH) states. These states support non-Abelian excitations from which protected quantum gatesExpand
Quantum dots as parafermion detectors
Parafermionic zero modes, Zn-symmetric generalizations of the well-known Z2 Majorana zero modes, can emerge as edge states in topologically nontrivial strongly correlated systems displayingExpand
A Field Theoretical Approach Through Bosonisation
Research into a type of quasiparticles known as anyons has been an active branch of research ever since they where hypothesised to exist in two-dimensional materials in 1977. It was quickly shownExpand
Photonic simulation of parafermionic Berry-phase statistics and contextuality
Quasiparticle poisoning is the main obstacle towards the realization of Majorana-based quantum computation. Parafermions, a natural generalization of Majorana fermions, can encode topological quditsExpand
Topological Phases with Parafermions: Theory and Blueprints
We concisely review the recent evolution in the study of parafermions—exotic emergent excitations that generalize Majorana fermions and similarly underpin a host of novel phenomena. First weExpand
...
1
2
3
4
...

References

SHOWING 1-10 OF 40 REFERENCES
Introduction to Topological Quantum Computation
TLDR
The makings of anyonic systems, their properties and their computational power are presented in a pedagogical way and special emphasis is given to the motivation and physical intuition behind every mathematical concept. Expand
Flux-controlled quantum computation with Majorana fermions
uxes. We show that readout operations can also be fully ux-controlled, without requiring microscopic control over tunnel couplings. We identify the minimal circuit that can perform theExpand
Quantum mechanics : a modern development
Although there are many textbooks that deal with the formal apparatus of quantum mechanics (QM) and its application to standard problems, none take into account the developments in the foundations ofExpand
Hierarchical Mean-Field Theories
We present a systematic and reliable methodology, termed hierarchical mean-field theory (HMFT), to study and predict the behavior of strongly coupled many-particle systems. HMFT is a simpleExpand
Quantum Mechanics: Symbolism of Atomic Measurements
Prologue.- A. Fall Quarter: Quantum Kinematics.- 1 Measurement Algebra.- 2 Continuous q, p Degree of Freedom.- 3 Angular Momentum.- 4 Galilean Invariance.- B. Winter Quarter: Quantum Dynamics.- 5Expand
Ann
Aaron Beck’s cognitive therapy model has been used repeatedly to treat depression and anxiety. The case presented here is a 34-year-old female law student with an adjustment disorder with mixedExpand
Adv
  • Phys. 60, 679
  • 2011
Phys
  • Rev. Lett. 86, 1082 (2001); Adv. in Phys. 53, 1
  • 2004
Phys
  • 26, 2234
  • 1985
Annu
  • Rev. Con. Mat. Phys. 4, 113
  • 2013
...
1
2
3
4
...