Coherent propagation of quasiparticles in topological spin liquids at finite temperature

Abstract

The appearance of quasiparticle excitations with fractional statistics is a remarkable defining trait of topologically ordered systems. In this work, we investigate the experimentally relevant finite temperature regime in which one species of quasiparticle acts as a stochastic background for another, more energetically costly, species that hops coherently across the lattice. The nontrivial statistical angle between the two species leads to interference effects that we study using a combination of numerical and analytical tools. In the limit of self-retracing paths, we are able to use a Bethe lattice approximation to construct exact analytical expressions for the time evolution of the site-resolved density profile of a spinon initially confined to a single site. Our results help us to understand the temperature-dependent crossover from ballistic to quantum (sub-)diffusive behaviour as a consequence of destructive interference between lattice walks. The subdiffusive behaviour is most pronounced in the case of semionic mutual statistics, and it may be ascribed to the localised nature of the effective tight-binding description, an effect that is not captured by the Bethe lattice mapping. In addition to quantum spin liquids, our results are directly applicable to the dynamics of isolated holes in the large-$U$ limit of the Hubbard model, relevant to ultracold atomic experiments. A recent proposal to implement ${\mathbb{Z}}_2$ topologically ordered Hamiltonians using quantum annealers provides a further exciting avenue to test our results.

arXiv comment17 pages, 10 figures; updated figures in v2

References in corpus (36)

• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• A quantum gas microscope - detecting single atoms in a Hubbard regime optical lattice
• String-net condensation: A physical mechanism for topological phases
• Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
• Fractionalized excitations in the spin liquid state of a kagomé lattice antiferromagnet
• Kitaev quantum spin liquid - concept and materialization
• Spin-lattice coupling in frustrated antiferromagnets
• A Field Guide to Spin Liquids
• Theory of the spin bath
• Quantum Spin Ice: A Search for Gapless Quantum Spin Liquids in Pyrochlore Magnets
• Physics of the Kitaev model: fractionalization, dynamical correlations, and material connections
• Continuous excitations of the triangular-lattice quantum spin liquid YbMgGaO4
• Single-atom imaging of fermions in a quantum-gas microscope
• A Quantum Gas Microscope for Fermionic Atoms
• Evidence for a spinon Fermi surface in a triangular lattice quantum spin liquid candidate
• Site-resolved Imaging of Fermionic Lithium-6 in an Optical Lattice
• Fermionic response from fractionalization in an insulating two-dimensional magnet
• Thermal fractionalization of quantum spins in a Kitaev model: $T$-linear specific heat and coherent transport of Majorana fermions
• Imaging and addressing of individual fermionic atoms in an optical lattice
• Fractional Spin Fluctuation as a Precursor of Quantum Spin Liquids: Majorana Dynamical Mean-Field Study for the Kitaev Model
• Anderson localization due to random magnetic field in two dimensions
• Holes in the t-J_z model: a thorough study
• Effective Field Theory of the Random Flux Model
• Diffusion of electrons in random magnetic fields,
• Majorana dynamical mean-field study of spin dynamics at finite temperatures in the honeycomb Kitaev model
• Quantum correlations at infinite temperature: the dynamical Nagaoka effect
• Decoherence and Quantum Walks: anomalous diffusion and ballistic tails
• Temperature evolution of spin dynamics in two- and three-dimensional Kitaev models: Influence of fluctuating gauge fluxes
• Quantum Walk in Degenerate Spin Environments
• Field Theory of the Random Flux Model
• Hole motion in the Ising antiferromagnet: an application of the recursion method
• Observing spin fractionalization in the Kitaev spin liquid via temperature evolution of indirect resonant inelastic x-ray scattering
• Hydrogenic states of monopoles in diluted quantum spin ice
• Spectrum of itinerant fractional excitations in quantum spin ice
• New Kinds of Quantum Statistics

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• Experimental Realization of Classical ${\mathbb{Z}}_2$ Spin Liquids in a Programmable Quantum Device
• Subdiffusive dynamics and critical quantum correlations in a disorder-free localized Kitaev honeycomb model out of equilibrium
• Topologically stable ergodicity breaking from emergent higher-form symmetries in generalized quantum loop models
• Correlation holes and slow dynamics induced by fractional statistics in gapped quantum spin liquids
• Finite Temperature Dynamics in 0-Flux and $\pi$-Flux Quantum Spin Ice: Self-Consistent Exclusive Boson Approach
• Anderson localization of emergent quasiparticles: Spinon and vison interplay at finite temperature in a ${\mathbb{Z}}_2$ gauge theory in three dimensions
• Probing fractional statistics in quantum simulators of spin liquid Hamiltonians
• Flux roughening in spin ice with mixed $\pm J$ interactions
• Transport in honeycomb lattice with random $\pi$-fluxes: implications for low-temperature thermal transport in the Kitaev spin liquids
• Probing anyonic statistics via Mach-Zehnder interferometry in quantum computers
• Effects of critical correlations on quantum percolation in two dimensions