# 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

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#### References

SHOWING 1-10 OF 40 REFERENCES

Introduction to Topological Quantum Computation

- Computer Science, Physics
- 2012

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

- Physics
- 2013

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 the… Expand

Quantum mechanics : a modern development

- Mathematics
- 1998

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 of… Expand

Hierarchical Mean-Field Theories

- Physics
- 2004

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 simple… Expand

Quantum Mechanics: Symbolism of Atomic Measurements

- Physics
- 2001

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.- 5… Expand

Ann

- 2005

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 mixed… Expand

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