The parastatistics of braided Majorana fermions

• URL: http://arxiv.org/abs/2312.06693v1
• Date: Sat, 9 Dec 2023 15:17:01 GMT
• Title: The parastatistics of braided Majorana fermions
• Authors: Francesco Toppan
• Abstract summary: The braided Majorana fermions are obtained in a graded Hopf algebra endowed with a braided tensor product. The values of $t$ at roots of unity are organized into levels which specify the number of braided Majorana fermions in a multiparticle sector.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $4\times 4$ braiding matrix $B_t$ 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.

Related papers

• Generating non-Clifford gate operations through exact mapping between Majorana fermions and $\mathbb{Z}_4$ parafermions [0.0]
  This paper establishes an exact mapping between Majorana fermions to $mathbbZ_4$ parafermions in systems under total parity non-conserving and total parity conserving setting. It is revealed that braiding of Majorana fermions may lead to non-Clifford quantum gates in the 4-dimensional qudit representation spanned by $mathbbZ_4$ parafermions.
  arXiv  Detail & Related papers  (2024-11-27T20:22:38Z)
• Volichenko-type metasymmetry of braided Majorana qubits [0.0]
  This paper presents different mathematical structures connected with the parastatistics of braided Majorana qubits. Mixed-bracket Heisenberg-Lie algebras are introduced.
  arXiv  Detail & Related papers  (2024-06-02T21:50:29Z)
• Geometry of degenerate quantum states, configurations of $m$-planes and invariants on complex Grassmannians [55.2480439325792]
  We show how to reduce the geometry of degenerate states to the non-abelian connection $A$. We find independent invariants associated with each triple of subspaces. Some of them generalize the Berry-Pancharatnam phase, and some do not have analogues for 1-dimensional subspaces.
  arXiv  Detail & Related papers  (2024-04-04T06:39:28Z)
• Dimension-free discretizations of the uniform norm by small product sets [45.85600902330814]
  A classical inequality of Bernstein compares the supremum norm of $f$ over the unit circle to its supremum norm over the sampling set of the $K$-th roots of unity. We show that dimension-free discretizations are possible with sampling sets whose cardinality is independent of $deg(f)$ and is instead governed by the maximum individual degree of $f$.
  arXiv  Detail & Related papers  (2023-10-11T22:46:09Z)
• Gain-loss-induced non-Abelian Bloch braids [0.0]
  Braid phase transition occurs when the gain-loss is tuned across exceptional point degeneracy. The proposed theory is conducive to synthesizing exceptional materials for applications in topological computation and information processing.
  arXiv  Detail & Related papers  (2023-06-22T17:23:09Z)
• Some Remarks on the Regularized Hamiltonian for Three Bosons with Contact Interactions [77.34726150561087]
  We discuss some properties of a model Hamiltonian for a system of three bosons interacting via zero-range forces in three dimensions. In particular, starting from a suitable quadratic form $Q$, the self-adjoint and bounded from below Hamiltonian $mathcal H$ can be constructed. We show that the threshold value $gamma_c$ is optimal, in the sense that the quadratic form $Q$ is unbounded from below if $gammagamma_c$.
  arXiv  Detail & Related papers  (2022-07-01T10:01:14Z)
• First quantization of braided Majorana fermions [0.0]
  A $mathbb Z$-graded qubit represents an even (bosonic) "vacuum state" Multiparticle sectors of $N$, braided, indistinguishable Majorana fermions are constructed via first quantization.
  arXiv  Detail & Related papers  (2022-03-03T15:43:38Z)
• Quantum double aspects of surface code models [77.34726150561087]
  We revisit the Kitaev model for fault tolerant quantum computing on a square lattice with underlying quantum double $D(G)$ symmetry. We show how our constructions generalise to $D(H)$ models based on a finite-dimensional Hopf algebra $H$.
  arXiv  Detail & Related papers  (2021-06-25T17:03:38Z)
• Matrix Quantization of Classical Nambu Brackets and Super $p$-Branes [0.5156484100374059]
  We present an explicit matrix algebra quantization of the algebra of volume-preserving diffeomorphisms of the $n$-torus. We approximate the corresponding classical Nambu brackets using $mathfraksl(Nlceilfracn2rceil,mathbbC)$-matrices equipped with the finite bracket given by the completely anti-symmetrized matrix product.
  arXiv  Detail & Related papers  (2021-03-11T13:44:57Z)
• BRST-BV Quantum Actions for Constrained Totally-Symmetric Integer HS Fields [77.34726150561087]
  A non-minimal constrained BRST-BV Lagrangian formulation is presented for totally symmetric massless HS fields in a $d$-dimensional Minkowski space. A Fock-space quantum action is constructed as a shift of the total generalized field-antifield vector by a variational derivative of the gauge-fixing Fermion $Psi$ in a total BRST-BV action.
  arXiv  Detail & Related papers  (2020-10-29T16:40:32Z)
• A Concentration of Measure and Random Matrix Approach to Large Dimensional Robust Statistics [45.24358490877106]
  This article studies the emphrobust covariance matrix estimation of a data collection $X = (x_1,ldots,x_n)$ with $x_i = sqrt tau_i z_i + m$. We exploit this semi-metric along with concentration of measure arguments to prove the existence and uniqueness of the robust estimator as well as evaluate its limiting spectral distribution.
  arXiv  Detail & Related papers  (2020-06-17T09:02:26Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.