Anyon braiding in semi-analytical fractional quantum Hall lattice models

Abstract

It has been demonstrated numerically, mainly by considering ground state properties, that fractional quantum Hall physics can appear in lattice systems, but it is very difficult to study the anyons directly. Here, I propose to solve this problem by using conformal field theory to build semi-analytical fractional quantum Hall lattice models having anyons in their ground states, and I carry out the construction explicitly for the family of bosonic and fermionic Laughlin states. This enables me to show directly that the braiding properties of the anyons are those expected from analytical continuation of the wave functions and to compute properties such as internal structure, size, and charge of the anyons with simple Monte Carlo simulations. The models can also be used to study how the anyons behave when they approach or even pass through the edge of the sample. Finally, I compute the effective magnetic field seen by the anyons, which varies periodically due to the presence of the lattice.

arXiv comment5+2 pages, 4 figures, v2: accepted version

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• Fusion channels of non-Abelian anyons from angular-momentum and density-profile measurements
• Characterization of quasiholes in fractional Chern insulators
• Quantum many-body scars with chiral topological order in 2D and critical properties in 1D
• Charge and statistics of lattice quasiholes from density measurements: a Tree Tensor Network study
• Lattice effects on Laughlin wave functions and parent Hamiltonians
• Characterization of quasiholes in two-component fractional quantum Hall states and fractional Chern insulators in $|C|=2$ flat bands
• Quasielectrons as inverse quasiholes in lattice fractional quantum Hall models
• Wave Functions for Fractional Chern Insulators on Disk Geometry
• Real-space probe for lattice quasiholes
• Parent Hamiltonian Reconstruction of Jastrow-Gutzwiller Wavefunctions
• Continuum limit of lattice models with Laughlin-like ground states containing quasiholes
• Non-Abelian quasiholes in lattice Moore-Read states and parent Hamiltonians
• Lattice Laughlin states on the torus from conformal field theory
• Chiral conformal field theory for topological states and the anyon eigenbasis on the torus
• Squeezing anyons for braiding on small lattices
• Model wavefunctions for an interface between lattice Laughlin and Moore-Read states
• Adiabatic time evolution of highly excited states
• Anyonic quasiparticles of hardcore anyons
• Continuum limit of lattice quasielectron wavefunctions
• Approximate Hofstadter- and Kapit-Mueller-like parent Hamiltonians for Laughlin states on fractals
• Bridging conformal field theory and parton approaches to SU(n)_k chiral spin liquids