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arXiv:1909.08633 · Physical review. B./Physical review. B

Coherent propagation of quasiparticles in topological spin liquids at finite temperature

Oliver Hart, Yuan Wan, Claudio Castelnovo

Published Feb 26, 2020• 22 citations
arXivHTMLPDF

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 behavior as a consequence of destructive interference between lattice walks. The subdiffusive behavior is most pronounced in the case of semionic mutual statistics, and it may be ascribed to the localized 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.

DOI
10.1103/physrevb.101.064428

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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 behavior as a consequence of destructive interference between lattice walks. The subdiffusive behavior is most pronounced in the case of semionic mutual statistics, and it may be ascribed to the localized 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-UUU limit of the Hubbard model, relevant to ultracold atomic experiments. A recent proposal to implement Z2{\mathbb{Z}}_{2}Z2​ topologically ordered Hamiltonians using quantum annealers provides a further exciting avenue to test our results.
Abstract: Realistic model Hamiltonians for quantum spin liquids frequently exhibit a large separation of energy scales between their elementary excitations. At intermediate, experimentally relevant temperatures, some excitations are sparse and hop coherently, whereas others are thermally incoherent and dense. Here, we study the interplay of two such species of quasiparticle, dubbed spinons and visons, which are subject to nontrivial mutual statistics – one of the hallmarks of quantum spin liquid behaviour. Our results for Z2 quantum spin liquids show an intriguing feedback mechanism, akin to the Nagaoka effect, whereby spinons become localised on temperature-dependent patches of expelled visons. This phenomenon has important consequences for the thermodynamic and transport properties of the system, as well as for its response to quenches in temperature. We argue that these effects can be measured in experiments and may provide viable avenues for obtaining signatures of quantum spin liquid behaviour.
Fractional statistics of quasiparticle excitations often plays an important role in the detection and characterization of topological systems. In this paper, we investigate the case of a three-dimensional (3D) Z2{\mathbb{Z}}_{2}Z2​ gauge theory, where the excitations take the form of bosonic spinon quasiparticle and vison flux tubes, with mutual semionic statistics. We focus on an experimentally relevant intermediate temperature regime, where sparse spinons hop coherently on a dense quasistatic and stochastic vison background. The effective Hamiltonian reduces to a random-sign bimodal tight-binding model, where both the particles and the disorder are borne out of the same underlying quantum spin liquid (QSL) degrees of freedom, and the coupling between the two is purely driven by the mutual fractional statistics. We study the localization properties and observe a mobility edge located close to the band edge, whose transition belongs to the 3D Anderson model universality class. Spinons allowed to propagate through the quasistatic vison background appear to display quantum diffusive behavior. When the visons are allowed to relax, in response to the presence of spinons in equilibrium, we observe the formation of vison depletion regions slave to the support of the spinon wave function. We discuss how this behavior can give rise to measurable effects in the relaxation, response, and transport properties of the system and how these may be used as signatures of the mutual semionic statistics and as precursors of the QSL phase arising in the system at lower temperatures.
Realistic model Hamiltonians for quantum spin liquids frequently exhibit a large separation of energy scales between their elementary excitations. At intermediate, experimentally relevant temperatures, some excitations are sparse and hop coherently, whereas others are thermally incoherent and dense. Here, we study the interplay of two such species of quasiparticle, dubbed spinons and visons, which are subject to nontrivial mutual statistics - one of the hallmarks of quantum spin liquid behaviour. Our results for [Formula: see text] quantum spin liquids show an intriguing feedback mechanism, akin to the Nagaoka effect, whereby spinons become localised on temperature-dependent patches of expelled visons. This phenomenon has important consequences for the thermodynamic and transport properties of the system, as well as for its response to quenches in temperature. We argue that these effects can be measured in experiments and may provide viable avenues for obtaining signatures of quantum spin liquid behaviour.
Relaxation processes in topological phases such as quantum spin liquids are controlled by the dynamics and interaction of fractionalized excitations. In layered materials hosting two-dimensional topological phases, elementary quasiparticles can diffuse freely within the layer, whereas only pairs (or more) can hop between layers - a fundamental consequence of topological order. Using exact solutions of emergent nonlinear diffusion equations and particle-based stochastic simulations, we explore how pump-probe experiments can provide unique signatures of the presence of 2d2d2d topological excitations in a 3d3d3d material. Here we show that the characteristic time scale of such experiments is inversely proportional to the initial excitation density, set by the pump intensity. A uniform excitation density created on the surface of a sample spreads subdiffusively into the bulk with a mean depth zˉ\bar zzˉ scaling as ∼t1/3\sim t^{1/3}∼t1/3 when annihilation processes are absent. The propagation becomes logarithmic, zˉ∼log⁡t\bar z \sim \log tzˉ∼logt, when pair-annihilation is allowed. Furthermore, pair-diffusion between layers leads to a new decay law for the total density, n(t)∼(log⁡2t)/tn(t) \sim (\log^2 t)/tn(t)∼(log2t)/t - slower than in a purely 2d2d2d system. We discuss possible experimental implications for pump-probe experiments in samples of finite width.
Relaxation processes in topological phases such as quantum spin liquids are controlled by the dynamics and interaction of topological excitations. In layered materials hosting two-dimensional topological order, elementary quasiparticles can diffuse freely within the layer, whereas only pairs (or more) can hop between layers - a fundamental consequence of topological order. Using exact solutions of emergent nonlinear classical diffusion equations and particle-based stochastic simulations, we explore how pump-probe experiments can provide unique signatures of the presence of 2d 2 d topological excitations in a layered 3d 3 d material. Here we show that the characteristic time scale of such experiments is inversely proportional to the initial excitation density, set by the pump intensity. A uniform excitation density created on the surface of a sample spreads subdiffusively into the bulk with a mean depth \bar z z ‾ scaling as \sim t^{1/3} ∼ t 1 / 3 when annihilation processes are absent. The propagation becomes logarithmic, \bar z \sim \log t z ‾ ∼ log ⁡ t , when pair-annihilation is allowed. Furthermore, pair-diffusion between layers leads to a new decay law for the total density, n(t) \sim (\log^2 t)/t n ( t ) ∼ ( log ⁡ 2 t ) / t - slower than in a purely 2d 2 d system. We discuss possible experimental implications for pump-probe experiments in finite-size systems.
Frustrated spin-ice systems support emergent gauge fields and fractionalized quasiparticles that act as magnetic monopoles. Although artificial platforms have enabled their direct visualization, access to their quantum-coherent dynamics has remained limited. Here we realize a programmable dipolar square spin-ice model using a superconducting-qubit quantum annealer, providing access to a previously unexplored quantum-coherent regime of artificial spin ice. By implementing a direct one-to-one mapping between lattice spins and physical qubits, together with engineered extended couplings, we realize effective dipolar interactions on frustrated lattices comprising more than 400 vertices. Tuning transverse-field fluctuations enables us to probe the real-time dynamics of Dirac-string defects and interacting monopole plasmas. We observe super-diffusive monopole transport, with scaling exponents intermediate between classical diffusion and ballistic motion, indicating dynamics beyond classical stochastic relaxation and consistent with coherent propagation within an emergent gauge manifold. These results establish programmable quantum spin ice as a scalable platform for investigating fractionalized excitations and emergent gauge dynamics in engineered quantum matter.