Effective models of doped quantum ladders of non-Abelian anyons

Abstract

Quantum spin models have been studied extensively in one and higher dimensions. Furthermore, these systems have been doped with holes to study t-J models of SU (2) spin-1/2. Their anyonic counterparts can be built from non-Abelian anyons, such as Fibonacci anyons described by SU (2)3 theories, which are quantum deformations of the SU (2) algebra. Inspired by the physics of SU (2) spins, several works have explored ladders of Fibonacci anyons and also one-dimensional (1D) t-J 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 t-J (or modified t-J-V ) 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 t-J 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 τ 's and light τ '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 τ '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.

The eigenstate thermalization hypothesis in constrained Hilbert spaces: A case study in non-Abelian anyon chains

“…It would be interesting to test these expectations in general anyon models and in 2D, and in particular to explore thermalization in itinerant anyons, as discussed for example in Refs. [62,63]. We note that the fusion tree basis obtained by enumerating the anyons and ordering them into a line is not illuminating for the question of thermalization in 2D as the Hamiltonian appears nonlocal in this basis.…”

“…73,74 . We note that the fusion tree basis obtained by enumerating the anyons and ordering them into a line is not illuminating for the question of thermalization in 2D as the Hamiltonian appears nonlocal in this basis.…”

Anyonic quasiparticles of hardcore anyons

“…Using a generalized Jordan-Wigner construction, one can build anyonic oscillators on a 2D square lattice [32], which explains the relations of such systems with quantum groups and q deformations of classical Lie algebras. In a similar vein, it is possible to construct chain or ladder models that are equipped with anyonic degrees of freedom and investigate the properties of these systems [33][34][35][36][37][38][39][40][41].…”

Phase transitions on a ladder of braided non-Abelian anyons

“…In Ref. 31, the authors studied two and three leg ladders of Fibonacci anyons, where the anyons could interact and braid with one another. There, the focus was on the strong rung coupling regime where the rung hopping is greater than the leg hoping and their results showed that those models can be essentially mapped onto one dimensional physics of itinerant hard-core anyons.…”