Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2512.08712

Diffusion and relaxation of topological excitations in layered spin liquids

Joy, Aprem P., Lange, Roman, Rosch, Achim

Published Dec 9, 2025• 0 citations
arXivHTMLPDF

Abstract

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 $2d$ topological excitations in a $3d$ 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 $\bar z$ scaling as $\sim t^{1/3}$ when annihilation processes are absent. The propagation becomes logarithmic, $\bar z \sim \log t$, when pair-annihilation is allowed. Furthermore, pair-diffusion between layers leads to a new decay law for the total density, $n(t) \sim (\log^2 t)/t$ - slower than in a purely $2d$ system. We discuss possible experimental implications for pump-probe experiments in samples of finite width.

DOI
10.48550/arxiv.2512.08712

Related papers

Diffusion and relaxation of topological excitations in layered spin liquids

Aprem P. Joy, Roman Lange, Achim Rosch

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.

SciPost Physics•Jun 25, 2026•0 citations

Anomalous thermal relaxation and pump-probe spectroscopy of two-dimensional topologically ordered systems

Max McGinley, Michele Fava, S. A. Parameswaran

We study the behavior of linear and nonlinear spectroscopic quantities in two-dimensional topologically ordered systems, which host anyonic excitations exhibiting fractional statistics. We highlight the role that braiding phases between anyons have on the dynamics of such quasiparticles, which as we show dictates the behavior of both linear response coefficients at finite temperatures, as well as nonlinear pump-probe response coefficients. These quantities, which act as probes of temporal correlations in the system, are shown to obey distinctive universal forms at sufficiently long timescales. As well as providing an experimentally measurable fingerprint of anyonic statistics, the universal behavior that we find also demonstrates anomalously fast thermal relaxation: correlation functions decay as a “squished exponential” C ( t ) ∼ exp ( − [ t / τ ] 3 / 2 ) at long times. We attribute this unusual asymptotic form to the nonlocal nature of interactions between anyons, which allows relaxation to occur much faster than in systems with quasiparticles interacting via local, nonstatistical interactions. While our results apply to any Abelian or non-Abelian topological phase in two-dimensions, we discuss in particular the implications for candidate quantum spin liquid materials, wherein the relevant quantities can be measured using pre-existing time-resolved terahertz-domain spectroscopic techniques. Published by the American Physical Society 2024

arXiv:2402.06484•Physical review. B./Physical review. B•Feb 6, 2024•6 citations

Coherent propagation of quasiparticles in topological spin liquids at finite temperature

Oliver Hart, Yuan Wan, Claudio Castelnovo

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.

arXiv:1909.08633•Physical review. B./Physical review. B•Feb 26, 2020•22 citations

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

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.

arXiv:2209.00601•Physical Review Research•Dec 23, 2022•5 citations

Probing fractional statistics in quantum simulators of spin liquid Hamiltonians

Shiyu Zhou, Maria Zelenayova, Oliver Hart +2 more

Recent advances in programmable quantum devices brought to the fore the intriguing possibility of using them to realise and investigate topological quantum spin liquid phases. This new and exciting direction brings about important research questions on how to probe and determine the presence of such exotic, highly entangled phases in a noisy quantum environment. One of the most promising tools is investigating the behaviour of the topological excitations, and in particular their fractional statistics. In this work we put forward a generic route to achieve this, and we illustrate it in the specific case of \mathbb{Z}_2 ℤ 2 topological spin liquids implemented with the aid of combinatorial gauge symmetry. We design a convenient architecture to study signatures of fractional statistics via quasiparticle interferometry, and we assess its robustness to diagonal and off-diagonal disorder, as well as to dephasing - effects that are generally pervasive in current quantum programmable devices. Interestingly, when turned on its head, our scheme provides a remarkably clear test of the “quantumness” of these devices, with robust signatures that crucially hinge on quantum coherence and quantum interference effects, and cannot be mimicked by classical stochastic processes.

arXiv:2211.09784•SciPost Physics•Nov 14, 2023•5 citations

Theory of Two-Dimensional Nonlinear Spectroscopy for the Kitaev Spin Liquid

Wonjune Choi, Ki Hoon Lee, Yong Baek Kim

Unambiguous identification of fractionalized excitations in quantum spin liquids has been a long-standing issue in correlated topological phases. Conventional spectroscopic probes, such as the dynamical spin structure factor, can only detect composites of fractionalized excitations, leading to a broad continuum in energy. Lacking a clear signature in conventional probes has been the biggest obstacle in the field. In this work, we theoretically investigate what kinds of distinctive signatures of fractionalized excitations can be probed in two-dimensional nonlinear spectroscopy by considering the exactly solvable Kitaev spin liquids. We demonstrate the existence of a number of salient features of the Majorana fermions and fluxes in two-dimensional nonlinear spectroscopy, which provide crucial information about such excitations.

arXiv:1911.07138•Physical Review Letters•Mar 20, 2020•67 citations
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.
We study the behavior of linear and nonlinear spectroscopic quantities in two-dimensional topologically ordered systems, which host anyonic excitations exhibiting fractional statistics. We highlight the role that braiding phases between anyons have on the dynamics of such quasiparticles, which as we show dictates the behavior of both linear response coefficients at finite temperatures, as well as nonlinear pump-probe response coefficients. These quantities, which act as probes of temporal correlations in the system, are shown to obey distinctive universal forms at sufficiently long timescales. As well as providing an experimentally measurable fingerprint of anyonic statistics, the universal behavior that we find also demonstrates anomalously fast thermal relaxation: correlation functions decay as a “squished exponential” C ( t ) ∼ exp ( − [ t / τ ] 3 / 2 ) at long times. We attribute this unusual asymptotic form to the nonlocal nature of interactions between anyons, which allows relaxation to occur much faster than in systems with quasiparticles interacting via local, nonstatistical interactions. While our results apply to any Abelian or non-Abelian topological phase in two-dimensions, we discuss in particular the implications for candidate quantum spin liquid materials, wherein the relevant quantities can be measured using pre-existing time-resolved terahertz-domain spectroscopic techniques. Published by the American Physical Society 2024
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.
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.
Recent advances in programmable quantum devices brought to the fore the intriguing possibility of using them to realise and investigate topological quantum spin liquid phases. This new and exciting direction brings about important research questions on how to probe and determine the presence of such exotic, highly entangled phases in a noisy quantum environment. One of the most promising tools is investigating the behaviour of the topological excitations, and in particular their fractional statistics. In this work we put forward a generic route to achieve this, and we illustrate it in the specific case of \mathbb{Z}_2 ℤ 2 topological spin liquids implemented with the aid of combinatorial gauge symmetry. We design a convenient architecture to study signatures of fractional statistics via quasiparticle interferometry, and we assess its robustness to diagonal and off-diagonal disorder, as well as to dephasing - effects that are generally pervasive in current quantum programmable devices. Interestingly, when turned on its head, our scheme provides a remarkably clear test of the “quantumness” of these devices, with robust signatures that crucially hinge on quantum coherence and quantum interference effects, and cannot be mimicked by classical stochastic processes.
Unambiguous identification of fractionalized excitations in quantum spin liquids has been a long-standing issue in correlated topological phases. Conventional spectroscopic probes, such as the dynamical spin structure factor, can only detect composites of fractionalized excitations, leading to a broad continuum in energy. Lacking a clear signature in conventional probes has been the biggest obstacle in the field. In this work, we theoretically investigate what kinds of distinctive signatures of fractionalized excitations can be probed in two-dimensional nonlinear spectroscopy by considering the exactly solvable Kitaev spin liquids. We demonstrate the existence of a number of salient features of the Majorana fermions and fluxes in two-dimensional nonlinear spectroscopy, which provide crucial information about such excitations.