You are an expert at summarizing long articles. Proceed to summarize the following text: 
quantum statistics is an important aspect of quantum mechanics and it lays down the rules for identifying different classes of particles . in three dimensions , the exchange of two particles in a quantum system can result in a phase change of either 0 or @xmath6 for the wave function , leading to bosons and fermions . the scenario is very different in two - dimensions ( 2d ) and it is well known that such quantum systems give rise to anyonic quasiparticle excitations.@xcite these anyons are observed as excitations , localized disturbances of the ground state in systems with topological order . rich behavior emerges especially for non - abelian anyons , for which the exchange of two anyons is described by a unitary matrix.@xcite    models of interacting non - abelian anyons draw motivation from quantum spin models , and in particular the heisenberg model , which has been studied for a wide range of lattices including one - dimension ( 1d ) chains and ladders of @xmath2 spins . non - abelian anyons can be described as so - called quantum deformations of the usual @xmath2 spins . formally , they are described by @xmath7 chern - simons theories . these @xmath7 theories are obtained by ` deforming ' the @xmath2 algebra so as to retain only the first @xmath8 representations . the most widely studied models are the @xmath9 and @xmath10 theories that describe ` ising ' and ` fibonacci ' anyons respectively . non - abelian anyons are expected to be present in topologically ordered systems including certain fractional quantum hall states,@xcite @xmath11-wave superconductors,@xcite spin models,@xcite solid state heterostructures@xcite and rotating bose - einstein condensates.@xcite in particular , fibonacci anyons occur as quasi holes in the @xmath12 read - rezayi state which might be able to describe the @xmath13 fractional quantum hall state.@xcite while several experiments have shown evidence for emergent majorana modes,@xcite experimental evidence of fibonacci anyons is yet to come .    in the absence of interactions , non - abelian anyons have an exponentially degenerate ground state manifold . on this ground state manifold exchange ( braiding ) of non - abelian anyons acts in a non - commutative way , by bringing about a non - trivial transformation in the degenerate manifold of the many - quasiparticle hilbert space . this has generated interest since it can be used for topological fault - tolerant quantum computation.@xcite    interactions between non - abelian anyons can be modeled by generalizations of the spin-1/2 heisenberg model . these models have been studied for chains of fibonacci anyons@xcite including nearest neighbour couplings@xcite and also longer range couplings@xcite have been studied . chains of higher spin quasiparticles have also been explored,@xcite critical phases have been identified and the corresponding conformal field theory ( cft ) has been obtained from numerical simulations.@xcite the effect of disorder for chains of fibonacci anyons has been investigated.@xcite    as a step towards understanding the collective behavior of itinerant non - abelian anyons , these chains can be doped with mobile holes , inspired by the electronic @xmath0@xmath1 model.@xcite electrons confined in 1d can exhibit the phenomenon of `` spin - charge separation '' , where the spectrum can be interpreted in terms of two independent pieces , one arising from electric charge without spin , and the other from a spinon without any charge.@xcite analogously low - energy effective @xmath0@xmath1 models have been analyzed for the case of doped chains of fibonacci ( and ising ) anyons . these models exhibit a fractionalization of the spectrum into charge and anyonic degrees of freedom,@xcite an extension of a phenomenon that exists in luttinger liquids.@xcite    as a step towards two dimensions , anyon models have been investigated on chains coupled to form so - called quantum _ ladders _ of non - abelian anyons , which provide anyonic generalizations of the 2d quantum magnets.@xcite    in this paper , we combine the models mentioned above , by studying _ doped _ quantum ladders of fibonacci anyons consisting of two or three chains . the structure of the rest of the paper is as follows : section  [ model ] begins with a brief introduction of non - abelian anyons and introduces our model . in section  [ isolated_rungs ] , we discuss the strong rung coupling limit drawing analogy with the spin ladder models , listing out all the possible quantum states and the phase diagram for the model under study . in section [ coupled_rungs ] , we list all the phases that arise for weakly coupled rungs . the subsequent sections are dedicated to the discussion of all these phases . section [ sec : effpaired ] discusses the hard - core boson models and section [ sec : effgolden ] describes the golden chain phases . in section [ sec : efftj ] , we analyse the effective @xmath14 models for two and three - leg ladders , presenting the numerical results for the same . we extend the phenomenon of spin - charge separation to ( doped ) ladders of fibonacci anyons . in section  [ fm_rungs ] , we introduce a new model of heavy and light fibonacci anyons that is obtained for certain density regimes when the rung couplings are fm . we conclude by summarising our results in section  [ conclude ] . in this paper we focus on fibonacci anyons that are described by the @xmath3 theories . @xmath7 chern - simons theories@xcite are so - called quantum deformations of the @xmath2 algebra . their degrees of freedom are encoded by @xmath15topological charges @xmath16 , which are generalized angular momenta . in contrast to @xmath2 , in @xmath7 theories the total ` spin ' @xmath16 is limited to be @xmath17 . akin to the tensor product of spins , non - abelian anyons can be @xmath15fused according to fusion rules given by @xmath18    for example , for the fusion of two anyons with @xmath19 , these rules would mean @xmath20 ( for @xmath21 ) . similarly , for the case of fibonacci anyons @xmath22 , when @xmath23 the fusion rule reads as @xmath24 . note that this is different from what one would obtain under a tensor product of @xmath2 spin-1 particles . in the limit @xmath25 , however , we recover the @xmath2 algebra and the rule simply describes the tensor product of two ordinary @xmath2 spins . ( that can be either or @xmath26 ) and bond labels @xmath27 . ( b ) the flat version of the fusion tree . ( c ) a basis change to a different fusion tree using an @xmath28-move . , title="fig : " ] 0.4truecm   ( that can be either or @xmath26 ) and bond labels @xmath27 . ( b ) the flat version of the fusion tree . ( c ) a basis change to a different fusion tree using an @xmath28-move . , title="fig : " ]    in the rest of this manuscript , we focus only to the fibonacci theory with @xmath10 , unless otherwise stated . there the allowed values for the topological charges are @xmath29 . but if we look closely at the fusion rules , we can make the identification @xmath30 and @xmath31 . thus , the fibonacci theory has two distinct types of _ particles _ which we denote as @xmath26 for the trivial particle with @xmath32 and @xmath5 for the fibonacci anyon with @xmath33 respectively . using these , the fusion rules read @xmath34    we represent a system of @xmath35 anyons by means of a _ fusion tree _ as shown in fig . [ fig:3figs](a ) , where the anyonic charges of the individual anyons are labelled by @xmath36 . the fusion outcome of successive fusion of the anyons are encoded by the ` bond ' labels ( links ) in the fusion tree , labelled by @xmath27 in fig . [ fig:3figs](a ) . the constraints on the bond labels due to fusion rules which must be satisfied at each vertex significantly reduce the size of the internal hilbert space . for @xmath35 fibonacci anyons ( @xmath5 ) the hilbert space grows asymptotically as @xmath37 where @xmath38 is the golden ratio . from now on we draw a flat version of the fusion tree , as shown in fig . [ fig:3figs](b ) .    to perform an operation on nearest neighbor anyons , it is advantageous to change to a different basis in which the two - particle fusion outcome is explicit . this is done via the @xmath28-move shown schematically in fig . [ fig:3figs](c ) . the @xmath28-move depends on the two site labels @xmath36 and @xmath39 and the bond labels @xmath40 and @xmath41 . if at least one of these four labels is @xmath26 , then there is only one choice of bond labels that satisfies the fusion algebra and the @xmath28-move is trivial . a non - trivial matrix is obtained only when all the four labels are anyons . specialising to the case where @xmath42 , the labels for the three bonds @xmath43 allowed by the fusion rules are @xmath44 which transforms to a new basis @xmath45 after the @xmath28-move : @xmath46 using these bases the @xmath28-matrix is represented as , @xmath47 where as mentioned above we have a non - trivial @xmath48 submatrix only when also @xmath49 . another operation that we need to perform on nearest neighbor anyons is that of exchanging ( or braiding ) them . in fig . [ fig : r ] , we show our convention for a right - handed braid . the left - hand braiding is the inverse of the process shown here . under a right - handed braid anyons @xmath50 and @xmath51 pick up a phase @xmath52 depending on the anyon types , @xmath50 and @xmath51 , that are undergoing an exchange and their fusion outcome @xmath53 . note that whenever @xmath50 or @xmath51 are @xmath54 , the phase is trivial . non - trivial phases are only obtained are for @xmath55 : @xmath56    in order to implement a braid on the standard fusion tree , we first have to change basis using an @xmath28-move to make the fusion outcome of the two anyons explicit , and then braid . this process is shown schematically in fig . [ fig : frf ] . this is represented by a braid matrix @xmath57 acting on the bond labels @xmath43 . the only non - trivial braid matrix is obtained when both the sites are occupied by anyons . in the basis of eq . ( [ eq : basis ] ) we obtain :    @xmath58    note that when the two site labels are a @xmath59 and a @xmath5 , the @xmath28-moves and the exchange phases are all trivial . the braid matrix is effectively the hopping of the anyon to the adjacent site . when both the site labels are @xmath59 , the braid matrix is simply given by the identity matrix .      in this section we review the so - called ` golden chains ' , consisting of 1d arrays of localized fibonacci anyons with pairwise interactions between nearest neighbors.@xcite in this model the hamiltonian for the magnetic interactions between anyons is defined in analogy to the heisenberg exchange interaction . we assign an energy @xmath60 if the fusion outcome of two interacting anyons is trivial . for afm couplings @xmath61 , this favours the fusion outcome of two neighbouring anyons to be trivial , while for fm couplings @xmath62 , the fusion of two anyons is preferred to be @xmath5 . this interaction between nearest neighbor anyons is depicted schematically in fig . [ fig : tj](a ) and is implemented by projecting on the identity fusion channel @xmath63 where @xmath28 is the operator corresponding to the @xmath28-move ( see eq . ( [ eq : f ] ) ) and @xmath64 is an operator that projects onto the @xmath26 state . in the basis of eq . ( [ eq : basis ] ) , the matrix representation for the ( dimensionless ) magnetic interaction can be written explicitly as : @xmath65    . ( b ) the kinetic hopping ( of amplitude @xmath0 ) of an anyon to its nearest neighbor vacant site . the blue circles represent anyons while the white circles denote vacant sites or holes . ]    golden chains with afm couplings are described by the @xmath10 restricted solid on solid ( rsos ) model which is a cft with central charge @xmath66 . for ferromagnetic couplings the corresponding cft is that of the critical 3-state potts model with @xmath67.@xcite      to model itinerant anyons we introduce holes , _ i.e. _ sites with a trivial anyon @xmath68 on some of the sites . the holes and @xmath5 anyons are labelled by different @xmath69 ( electric ) charges and anyonic ( non - abelian ) charges . the @xmath5 anyons ( referred to simply as ` anyons ' or ` particles ' hereafter ) can move on the chain which results in an additional kinetic energy contribution . this kinetic process is schematically shown in fig . [ fig : tj](b ) . it involves the hopping of a particle , along with its electric and anyonic charge to a neighbouring site . our specific model of itinerant anyons is a generalization of the electronic @xmath0@xmath1 model.@xcite assuming a large on - site charging energy , we eliminate the possibility of doubly occupied sites and allow anyons to only hop to empty sites . as in the case of electrons , the low - energy effective @xmath0@xmath1 model allows hopping of the anyons to nearest neighbor vacant sites and an exchange interaction between nearest neighbor anyons analogous to the heisenberg interactions explained above in sec .  [ goldenchain ] . the kinetic term can then be written as @xmath70 , where @xmath71 is the ( dimensionless ) operator corresponding to the nearest neighbor hopping process shown in fig . [ fig : tj](b ) . a @xmath0@xmath1 chain of itinerant anyons was studied for ising and fibonacci anyons,@xcite revealing a separation of excitations into charge and anyonic excitations , similar to spin - charge separation in its electronic counterpart . ladders of fibonacci anyons are formed by coupling chains of localized anyons.@xcite anyons interact with their nearest neighbors along the leg and rung directions via and @xmath72 . these interactions are shown schematically in fig . [ fig : ladder](a ) . as fusion path we choose the _ zig - zag path _ shown in fig . [ fig : ladder](b ) , since it minimizes the effective range of interactions on the fusion path . we choose periodic boundary conditions along the leg direction and open boundary conditions along the rungs .    with this choice of fusion path , nearest neighbor interactions on the rungs are also nearest neighbor along the fusion path , while those between anyons on the same leg are longer range along the fusion path . nearest neighbor rung interactions can be implemented in exactly the same way as for nearest neighbor on a chain ( see sec . [ goldenchain ] ) . in order to evaluate the interactions between particles on the same leg , we have to implement a change of basis , this time by braiding them in a clockwise manner until they are neighbours along the fusion path . this braiding is performed by the unitary braid matrix @xmath57 ( see eq .  ( [ eq : braid ] ) ) . once the particles are nearest neighbours along the path they can interact with the same term as discussed above in sec . [ goldenchain ] . after carrying out the interaction , the anyons have to be braided back to their original positions .    more specifically , for a two - leg ladder , adjacent anyons along the leg direction are next nearest neighbours along the fusion path ( see fig .  [ fig : ladder](b ) ) . thus , one needs to implement one braid operation . the hamiltonian for the magnetic interactions between nearest neighbor rungs @xmath73 and @xmath74 on the upper leg is given by @xmath75 and on the lower leg as @xmath76 where @xmath77 has been defined in eq . ( [ eq : hmag ] ) and @xmath73 labels the rungs ( so that @xmath78 labels the diagonal bonds along the path ) . in fig . [ fig : braid](a ) , we summarize the magnetic interactions between nearest neighbor along the leg direction for a two - leg ladder .    for a three - leg ladder , the leg interactions are longer ranged interactions , since adjacent anyons on a leg are third neighbours along the fusion path . thus , nearest neighbor leg interactions on a three - leg ladder ladder require two braids before particles are nearest neighbors on the fusion path.@xcite one gets for interaction between rungs @xmath73 and @xmath74 on the upper leg , @xmath79 on the middle leg , @xmath80 and on the lower leg , @xmath81 where @xmath82 labels the diagonal bonds along the path . the full magnetic hamiltonian on the legs is obtained by adding all contributions , @xmath83 , where @xmath84 is the number of legs . as an implementation detail we want to mention that the action of the operator @xmath85 can generate up to @xmath86 states for each bond interaction . the operator mixes spin labels , thus generates multiple images for each two - body interaction . this exponential increase in the number of resulting states leads to denser hamiltonian matrices as one increases the width @xmath84 of the ladder and restricts us from exploring larger system sizes .    for ladders of fibonacci anyons it was shown that similar odd - even effects as seen for @xmath2 spins continue to exist in the limit of strong afm rungs.@xcite afm coupled ladders of fibonacci anyons with even number of legs are gapped while those with odd number of legs are critical and are described by the same cft as the golden chain . on the other hand , fibonacci ladders with fm rung couplings are quite different from their @xmath2 counterparts.@xcite fibonacci ladders with a width that is a multiple of three are gapped since the rungs form singlets @xmath87 . other widths are gapless since the isolated rungs effectively form @xmath5 s , thereby yielding a gapless chain as the effective low - energy model . this is different from @xmath2 spins , for which an even number form a singlet ground state , and where thus all even width ladders are gapped .      in this paper we focus on itinerant ladders of fibonacci anyons . as schematically represented in fig . [ fig : ladder](a ) we denote the interaction strengths along the leg direction by and for the magnetic and kinetic terms respectively . along the perpendicular direction , the couplings and denote respectively the magnetic and kinetic terms . the magnetic interactions for the ladder have already been described in the section  [ undoped ] and we thus only need to discuss the kinetic terms . once again , the two sites on a rung are adjacent on the fusion path and the hopping is thus implemented as for the 1d @xmath0@xmath1 chain ( see section  [ tj ] ) . for a particle and hole lying on adjacent sites on the same leg of the ladder , we need to , once again , braid the sites to bring them to adjacent positions on the fusion tree . for a two - leg ladder , the kinetic term between rungs @xmath73 and @xmath74 on the upper leg is given by @xmath88 and on the lower leg as @xmath89 where @xmath71 has been defined above and @xmath73 labels the rungs . in fig . [ fig : braid](b ) , we summarize the kinetic process between nearest neighbor sites along the leg direction for a two - leg ladder .    for a three - leg ladder , a particle and hole lying on adjacent sites on a leg are third neighbours along the fusion path . thus , nearest neighbor leg interaction on a three - leg ladder requires two braids before the particle and the hole are nearest neighbors on the fusion path . one gets for kinetic terms between rungs @xmath73 and @xmath74 on the upper leg , @xmath90 on the middle leg , @xmath91 and on the lower leg , @xmath92 where @xmath82 labels the diagonal bonds along the path . note that , in the above equations , some of the braids may be trivial , in contrast to the case of the magnetic interactions . the full kinetic hamiltonian on the legs is obtained by adding all contributions , @xmath93 . here , the action of the operator @xmath94 can generate up to @xmath95 states for each bond interaction . we also consider models with an additional rung charging term @xmath96 where @xmath97 is the number of anyons on a rung and @xmath98 is determined by the implicit chemical potential . [ fig : parabola ] shows the energy profile for a given rung composition on the ladder . for the three - leg ladder under consideration , this term acts pairwise between all the three possible pairs of particles that can exist on the three - site rung . assuming a charging energy which is much larger compared to the exchange energy , we can consider the limit @xmath99 . in this limit we can restrict our calculations to just two values of the occupation on the rung , @xmath100 and @xmath101 , with @xmath100 ranging from @xmath102 to @xmath103 . this reduces the hilbert space and thus allows us to perform simulations of larger ladders . our numerical simulations have been performed by exact diagonalization using the lanczos algorithm . we exploit periodic boundary conditions along the leg direction to implement translation symmetry . this allows us to block - diagonalize the hamiltonian into @xmath104 blocks labeled by the total momentum @xmath105 ( @xmath106 being an integer ) , which reduces the size of the hilbert space , which is the major limiting factor in the simulations , by a factor @xmath104 . s while white circles represent vacant sites . the @xmath69 and topological charges for the different configurations are denoted in the parenthesis . the superscript @xmath107 refers to the lying on the upper ( lower ) leg . ] analogous to standard electronic @xmath0@xmath1 ladders the physics of anyonic @xmath0@xmath1 ladders can be understood starting from the strong rung coupling limit.@xcite we thus begin by identifying the low - lying states of isolated rungs .    in fig . [ fig : eff_particles_2 ] , we show the five rung configurations on isolated rungs for a two - leg ladder , and the total @xmath69 and anyonic charges that are possible for these rung configurations . when there are two holes on a rung , both of these charges are trivially zero . when the rung is occupied by two particles , the net @xmath69 charge is 2 , however the topological charge may be either @xmath26 or @xmath108 , giving rise to two different quantum states @xmath109 ( named  heavy @xmath5 " ) and @xmath110 ( named  heavy hole "  an empty rung being a  light hole " ) . in the case when there is a single on the rung , it can be either on the upper or on the lower leg with charges denoted as @xmath111 and @xmath112 respectively . the corresponding quantum states are respectively @xmath113 and @xmath114 . the bonding and anti - bonding states @xmath115 ( named  light @xmath5 " ) are formed by linear superpositions of the configurations with charges @xmath116 and @xmath117 given by @xmath118    s while white circles represent vacant sites . the first labels in the parenthesis signify the @xmath69 charge , corresponding to the number of @xmath5 s present on each rung and the second refers to their fusion outcome . the superscripts @xmath119 refer to the positions of the on the different legs ( upper , middle , lower ) of the ladder . ]    for a three - leg ladder , many more states are possible , as shown in fig . [ fig : eff_particles_3 ] . when there is a single on the rung @xmath120 , the light @xmath5 " quantum states formed by linear superpositions of the three different positions of the particle are given by latexmath:[\ ] ]      in addition to the above cases , we can also have a kinetic and potential terms when the difference in the @xmath69 charges on neighboring rungs is larger than 1 . such process occurs e.g. ( i ) between a charge-0 ( light ) hole and a charge-2 ( heavy ) hole ( marked by blue arrows in table .  [ table ] ) in the @xmath342 paired phase or ( ii ) between a charge-0 ( light ) hole and a charge-3 ( super heavy ) @xmath5 ( marked by orange arrows in table . [ table ] ) in the @xmath148 phase .    in case ( i ) , one needs to hop twice to be able to come back to a configuration @xmath343 that has the same @xmath69 charges as the initial configuration @xmath344 , so the effective hamiltonian ( leaving in the relevant subspace ) is obtained in second - order perturbation , in @xmath275@xcite @xmath345 where the sum is on the intermediate states corresponding to two ( light ) @xmath5 s on neighboring sites . the energy denominator is given by @xmath346 and matrix elements for all the intermediate states are ( @xmath347 ) so that one gets for @xmath348 a potential energy @xmath349 and for @xmath350 a hopping term @xmath351    in case ( ii ) , one needs to hop three times to be able to come back to a configuration that has the same @xmath69 charges as the initial configuration , so the effective hamiltonian is now obtained in third - order perturbation in @xmath275:@xcite where the intermediate states @xmath352 and @xmath353 carry a heavy hole and a light on neighboring rungs . the energy denominators given by the difference in energy between the initial ( degenerate with the final ) state and the intermediate states thus take the value @xmath354 starting from an initial state @xmath355 a simple hopping yields the intermediate state @xmath356 with the matrix elements given by for hopping on the upper leg @xmath357 on the middle leg , @xmath358 and on the lower leg , @xmath359 subsequently , a second hopping yields the intermediate state @xmath360 with hopping matrix elements on the upper leg @xmath361 on the middle leg , @xmath362 and on the lower leg , @xmath363 finally to come back to a state carrying the same @xmath69 charges on the rungs , the hopping amplitudes for the three legs are just the complex conjugate of those described in eqs . ( [ eq : t1u])-([eq : t1l ] ) , thus giving for @xmath348 a potential energy @xmath364 and for @xmath350 a hopping term @xmath365                                            r. s. k. mong , d. j. clarke , j. alicea , n. h. lindner , p. fendley , c. nayak , y. oreg , a. stern , e. berg , k. shten- gel , and m. p. a. fisher , universal topological quantum computation from a superconductor / abelian quantum hall heterostructure , phys . rev . x * 4 * , 011036 ( 2014 ) . v. mourik , k. zuo , s. m. frolov , s. r. plissard , e. p. a. m. bakkers , and l. p. kouwenhoven , signatures of majorana fermions in hybrid superconductor - semiconductor nanowire devices , science * 336 * , 1003 ( 2012 ) . a. das , y. ronen , y. most , y. oreg , m. heiblum , and h. shtrikman , zero - bias peaks and splitting in an al - inas nanowire topological superconductor as a signature of majorana fermions , nat . * 8 * , 887 ( 2012 ) . h. o. h. churchill , v. fatemi , k. grove - rasmussen , m. t. deng , p. caroff , h. q. xu , and c. m. marcus , superconductor - nanowire devices from tunneling to the multichannel regime : zero - bias oscillations and magnetoconductance crossover , phys . rev . b * 87 * , 241401 ( 2013 ) .                      c. gils , e. ardonne , s. trebst , a. w. w.ludwig , m. troyer , and z. wang , collective states of interacting anyons , edge states , and the nucleation of topological liquids , phys . rev . lett . * 103 * , 070401 ( 2009 ) . r. n. c. pfeifer , o. buerschaper , s. trebst , a. w. w. ludwig , m. troyer , and g. vidal , translation invariance , topology , and protection of criticality in chains of interacting anyons , phys . b * 86 * , 155111 ( 2012 ) .                          f. d. m. haldane , luttinger liquid theory of one - dimensional quantum fluids . i. properties of the luttinger model and their extension to the general 1d interacting spinless fermi gas , j. phys . c * 14 * , 2585 ( 1981 ) .                i. de p. r. moreira , n. suaud , n. guihry , j. p. malrieu , r. caballol , j. m. bofill , and f. illas , derivation of spin hamiltonians from the exact hamiltonian : application to systems with two unpaired electrons per magnetic site , phys . rev . b * 66 * , 134430 ( 2002 ) .    jean paul malrieu , rosa caballol , carmen j. calzado , coende graaf , and nathalie guihry , magnetic interactions in molecules and highly correlated materials : physical content , analytical derivation , and rigorous extraction of magnetic hamiltonians , chem . rev . * 114 * , 429 - 492 ( 2014 ) .
quantum spin models have been studied extensively in one and higher dimensions . 
 furthermore , these systems have been doped with holes to study @xmath0@xmath1 models of @xmath2 spin-1/2 . 
 their anyonic counterparts can be built from non - abelian anyons , such as fibonacci anyons described by @xmath3 theories , which are quantum deformations of the @xmath2 algebra . 
 inspired by the physics of @xmath2 spins , several works have explored ladders of fibonacci anyons and also one - dimensional ( 1d ) @xmath0@xmath1 models . here 
 we aim to explore the combined effects of extended dimensionality and doping by studying ladders composed of coupled chains of interacting itinerant fibonacci anyons . 
 we show analytically that in the limit of strong rung couplings these models can be mapped onto effective 1d models . 
 these effective models can either be gapped models of hole pairs , or gapless models described by @xmath0@xmath1 ( or modified @xmath0@xmath1@xmath4 ) chains of fibonacci anyons , whose spectrum exhibits a fractionalization into charge and anyon degrees of freedom . 
 the charge degrees of freedom are described by the hardcore boson spectra while the anyon sector is given by a chain of localized interacting anyons . by using exact diagonalizations for two - leg and three - leg ladders , 
 we show that indeed the doped ladders show exactly the same behavior as that of @xmath0@xmath1 chains . in the strong ferromagnetic rung limit , 
 we can obtain a new model that hosts two different kinds of fibonacci particles - which we denote as the _ heavy _ @xmath5 s and _ light _ 
 @xmath5 s . 
 these two particle types carry the same ( non - abelian ) topological charge but different ( abelian ) electric charges . once again , we map the two - dimensional ladder onto an effective chain carrying these heavy and light @xmath5 s . 
 we perform a finite size scaling analysis to show the appearance of gapless modes for certain anyon densities whereas a topological gapped phase is suggested for another density regime .