Simulation of braiding anyons using Matrix Product States

Abstract

Anyons exist as point like particles in two dimensions and carry braid statistics which enable interactions that are independent of the distance between the particles. Except for a relatively few number of models which are analytically tractable, much of the physics of anyons remain still unexplored. In this paper, we show how U(1)-symmetry can be combined with the previously proposed anyonic Matrix Product States to simulate ground states and dynamics of anyonic systems on a lattice at any rational particle number density. We provide proof of principle by studying itinerant anyons on a one dimensional chain where no natural notion of braiding arises and also on a two-leg ladder where the anyons hop between sites and possibly braid. We compare the result of the ground state energies of Fibonacci anyons against hardcore bosons and spinless fermions. In addition, we report the entanglement entropies of the ground states of interacting Fibonacci anyons on a fully filled two-leg ladder at different interaction strength, identifying gapped or gapless points in the parameter space. As an outlook, our approach can also prove useful in studying the time dynamics of a finite number of nonabelian anyons on a finite two-dimensional lattice.

Revised version: 20 pages, 14 captioned figures, 2 new tables. We have moved a significant amount of material concerning symmetric tensors for anyons --- which can be found in prior works --- to Appendices in order to streamline our exposition of the modified Anyonic-U(1) ansatz

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Cited by in corpus (8)

• Introduction to topological quantum computation with non-Abelian anyons
• A programming guide for tensor networks with global $SU(2)$ symmetry
• Numerical simulation of non-abelian anyons
• Phase transitions on a ladder of braided non-Abelian anyons
• Fibonacci Numbers and the Golden Ratio in Biology, Physics, Astrophysics, Chemistry and Technology: A Non-Exhaustive Review
• Characterizing the Entanglement of Anyonic Systems using the Anyonic Partial Transpose
• Studies of braided non-Abelian anyons using anyonic tensor networks
• Phases of Interacting Fibonacci Anyons on a Ladder at Half-Filling