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arXiv:2209.00601 · Physical Review Research

Anderson localization of emergent quasiparticles: Spinon and vison interplay at finite temperature in a Z2 gauge theory in three dimensions

Minho Kim, Giuseppe De Tomasi, Claudio Castelnovo

Published Dec 23, 2022• 5 citations
arXivHTMLPDF

Abstract

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) ${\mathbb{Z}}_{2}$ 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.

DOI
10.1103/physrevresearch.4.043206

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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.
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.
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.
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.
Understanding the nonequilibrium relaxation dynamics of quantum spin liquids is an important and relatively unexplored frontier, where fractionalized quasiparticles and emergent gauge fields can give rise to dynamical behaviors far beyond those of conventional magnets. Here we study the relaxation dynamics of the Kitaev honeycomb model following a thermal quench, focusing on visons—gapped Z2{{\mathbb{Z}}}_{2}Z2​ flux excitations of the emergent gauge field in the Kitaev spin liquid. The long-time evolution is governed by the diffusion and pair annihilation of visons, with both the activation barrier for vison motion and the effective vison-vison interactions mediated by fractionalized Majorana fermions. The resulting open-system quantum dynamics, induced by coupling to a thermal bath, can be efficiently simulated using an effective kinetic Monte Carlo approach. We uncover a rich set of temperature-dependent dynamical regimes. With decreasing temperature, the relaxation crosses over from diffusion-limited annihilation to terminal-velocity–limited kinetics, and ultimately to pronounced dynamical arrest and freezing. We show that this freezing behavior is closely tied to the formation of long-lived, metastable 3×3\sqrt{3}\times \sqrt{3}3​×3​ vison crystals, which strongly suppress further annihilation. Remarkably, even in the absence of true long-range crystalline order, the system exhibits a hidden coarsening dynamics of vison superclusters associated with an emergent Z3{{\mathbb{Z}}}_{3}Z3​ symmetry.
We develop an exact map of all states and operators from two-dimensional lattices of spins-1/21/21/2 into lattices of fermions and bosons with mutual semionic statistical interaction that goes beyond previous dualities of Z2{\mathbb{Z}}_{2}Z2​ lattice gauge theories because it does not rely on imposing local conservation laws and captures the motion of ``charges'' and ``fluxes'' on equal footing. This map allows to explicitly compute the Berry phases for the transport of fluxes in a large class of symmetry-enriched topologically ordered states with emergent Z2{\mathbb{Z}}_{2}Z2​ gauge fields that includes chiral, nonchiral, Abelian or non-Abelian, that can be perturbatively connected to models where the visons are static and the emergent fermionic spinons have a noninteracting dispersion. The numerical complexity of computing such vison phases reduces, therefore, to computing overlaps of ground states of free-fermion Hamiltonians. Among other results, we establish numerically the conditions under which the Majorana-carrying flux excitation in Ising-topologically ordered states enriched by translations acquires the 0 or $\ensuremath{\pi}$ phase when moving around a single plaquette.
Quantum spin liquids are exotic phases of matter that are prevented from being frozen even at zero temperature, and appear disordered by local probes that monitor the subsystems. Driven by quantum fluctuations, topological spin liquids are manifested by their long-range entanglement, and are characterized by quasiparticles with fractional statistics. Here, we make contact of a 2D Rydberg ice to a QED vacuum of an ultra-high-finesse optical cavity, and dynamically promote the frustrated background field of the spin ice to a Z2\mathbb{Z}_2Z2​ spin liquid. We characterize the deconfined nature of the dynamical gauge theory residing in the strongly-correlated Rydberg matter with Wilsonian loops. We observe the proliferation of vison and spinon pairs by site-resolved fluorescence imaging, and detect the exchange statistical angle θtop∼π/2θ_{\text{top}}\simπ/2θtop​∼π/2 between the two anyons by monitoring the dynamical correlators of the fluctuating cavity photons. Our work provides the first microscopic detection of anyons in a topological quantum matter, and heralds the arrival of strongly-coupled many-body QED, where interacting matter and light are put on equal footing at the level of individual quanta.