First quantization of braided Majorana fermions

Toppan, Francesco

doi:10.1016/j.nuclphysb.2022.115834

Cited by 2 publications

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“…The [5] braided multiparticle quantization of Majorana fermions produces truncations of the spectra at certain values of t roots of unity. This feature points towards a relation between the braided tensor product framework here discussed and the representations of quantum groups at roots of unity where similar truncations, see [14,15], are observed.…”

Section: Discussionmentioning

confidence: 99%

“…Braided Majorana fermions have been intensively investigated since the [1] Kitaev's proposal that they can be used to encode the logical operations of a topological quantum computer which offers protection from decoherence (see also [2][3][4]). In this talk I present consequences and open questions about the parastatistics of 2 -graded braided Majorana qubits derived from the results of [5]; this paper applied to 2 -graded qubits the [6] framework of a graded Hopf algebra endowed with a braided tensor product. A nonvanishing complex braiding parameter t controls the spectra of multiparticle Majorana fermions.…”

Section: Introductionmentioning

confidence: 99%

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The parastatistics of braided Majorana fermions

Toppan

2023

SciPost Phys. Proc.

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This paper presents the parastatistics of braided Majorana fermions obtained in the framework of a graded Hopf algebra endowed with a braided tensor product. The braiding property is encoded in a t-dependent 4×4 braiding matrix B_tBt related to the Alexander-Conway polynomial. The nonvanishing complex parameter t defines the braided parastatistics. At t=1 ordinary fermions are recovered. The values of t at roots of unity are organized into levels which specify the maximal number of braided Majorana fermions in a multiparticle sector. Generic values of t and the t=-1 root of unity mimick the behaviour of ordinary bosons.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The parastatistics of braided Majorana fermions

Toppan

2023

SciPost Phys. Proc.

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Volichenko-type metasymmetry of braided Majorana qubits

Toppan

2024

J. Phys. A: Math. Theor.

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This paper presents different mathematical structures connected with the parastatistics of braided Majorana qubits and clarifies their role; in particular, "mixed-bracket" Heisenberg-Lie algebras are introduced. These algebras belong to a more general framework than the Volichenko algebras defined in 1990 by Leites-Serganova as metasymmetries which do not respect even/odd gradings and lead to mixed brackets interpolating ordinary commutators and anticommutators.In a previous paper braided Z2-graded Majorana qubits were first-quantized within a graded Hopf algebra framework endowed with a braided tensor product. The resulting system admits truncations at roots of unity and realizes, for a given integer s=2,3,4, ..., an interpolation between ordinary Majorana fermions (recovered at s=2) and bosons (recovered in the s →∞ limit); it implements a parastatistics where at most s-1 indistinguishable particles are accommodated in a multi-particle sector.The structures discussed in this work are:- the quantum group interpretation of the roots of unity truncations recovered from a (superselected) set of reps of the quantum superalgebra Uq(osp(1|2));- the reconstruction, via suitable intertwining operators, of the braided tensor products as ordinary tensor products(in a minimal representation, the N-particle sector of the braided Majorana qubits is described by 2N x 2N;- the introduction of mixed brackets for the braided creation/annihilation operators which define generalized Heisenberg-Lie algebras;- the s→∞ untruncated limit of the mixed-bracket Heisenberg-Lie algebras producing parafermionic oscillators;- (meta)symmetries of ordinary differential equations given by matrix Schrödinger equations in 0+1 dimension induced by the braided creation/annihilation operators;- in the special case of a third root of unity truncation, a nonminimal realization of the intertwining operators defines the systemas a ternary algebra.

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First quantization of braided Majorana fermions

Cited by 2 publications

References 58 publications

The parastatistics of braided Majorana fermions

The parastatistics of braided Majorana fermions

Volichenko-type metasymmetry of braided Majorana qubits

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