Phase transitions on a ladder of braided non-Abelian anyons

Abstract

Non-Abelian anyons can exist as point-like particles in two-dimensional systems, and have particle exchange statistics which are neither bosonic nor fermionic. Like in spin systems, the role of fusion (Heisenberg-like) interactions between anyons has been well studied. However, unlike our understanding of the role of bosonic and fermionic statistics in the formation of different quantum phases of matter, little is known concerning the effect of non-Abelian anyonic statistics. We explore this physics using an anyonic Hubbard model on a two-legged ladder which includes braiding and nearest neighbour Heisenberg interactions among anyons. We study two of the most prominent non-Abelian anyon models: the Fibonacci and Ising type. We discover rich phase diagrams for both anyon models, and show the different roles of their fusion and braid statistics. * babatunde.ayeni@mq.edu.au 1 R. B. Laughlin, Phys. Rev. Lett. 50, 1395Lett. 50, (1983. Halperin, Phys. Rev. Lett. 52, 1583 (1984. 3 E. Fradkin, Phys. Rev. Lett. 63, 322 (1989).

A Supersymmetry and Quantum Cryptosystem with Path Integral Approach in Biology

“…We redefine the loop braid group by adding some extra properties to them for visualizing the folding structure in the amino acids [21]. We can apply the anyon [22] states of the pair between DNA and RNA as braid groups in anyon-geneonic pair states in the genetic code. The codon can be related to a table of public keys which can release noncoding RNA [23] as the private key for correctly translating a DNA sequence into a folded protein for the specific docking site in the antigen-antibody immune system.…”

A constructive bulk-boundary correspondence using multi-scale symmetric tensor networks

“…As a proof of principle to demonstrate the code described in appendix D functions as expected I focused on replicating the results of a new anyonic model using the MERA [105]. This model has a Fibonacci symmetry as described in subsection 7.2.2, meaning we can interpret each site as containing either the vacuum or a Fibonacci particle.…”

“…The phase space of the µ − t plane has been mapped out and characterised into 6 different phases as in figure 7.3. This was done in [105] Optimisation of the results may have been possible, however with the time available when I was performing these calculations this was not able to be done. Options to optimise the algorithm could have included using the modified binary MERA in order to allow an increased bond dimension.…”

“…The order parameter is the filling fraction ν, the fraction of number of sites with a Fibonacci anyon on them. This diagram is reproduced with permission from[105].…”