TY - JOUR

T1 - Simulation of braiding anyons using matrix product states

AU - Ayeni, Moses

AU - Singh, Sukhbinder

AU - Pfeifer, Robert N C

AU - Brennen, Gavin K.

PY - 2016/4/20

Y1 - 2016/4/20

N2 - Anyons exist as pointlike 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 remains 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 non-Abelian anyons on a finite two-dimensional lattice.

AB - Anyons exist as pointlike 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 remains 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 non-Abelian anyons on a finite two-dimensional lattice.

UR - http://www.scopus.com/inward/record.url?scp=84964446979&partnerID=8YFLogxK

UR - http://purl.org/au-research/grants/arc/CE110001013

U2 - 10.1103/PhysRevB.93.165128

DO - 10.1103/PhysRevB.93.165128

M3 - Article

AN - SCOPUS:84964446979

VL - 93

SP - 1

EP - 18

JO - Physical Review B: covering condensed matter and materials physics

JF - Physical Review B: covering condensed matter and materials physics

SN - 2469-9950

IS - 16

M1 - 165128

ER -