Flux Excitations Research Articles

Probing Majorana Wave Functions in Kitaev Honeycomb Spin Liquids with Second-Order Two-Dimensional Spectroscopy.

Two-dimensional coherent terahertz spectroscopy (2DCS) emerges as a valuable tool to probe the nature, couplings, and lifetimes of excitations in quantum materials. It thus promises to identify unique signatures of spin liquid states in quantum magnets by directly probing properties of their exotic fractionalized excitations. Here, we calculate the second-order 2DCS of the Kitaev honeycomb model and demonstrate that distinct spin liquid fingerprints appear already in this lowest-order nonlinear response χ_{yzx}^{(2)}(ω_{1},ω_{2}) when using crossed light polarizations. We further relate the off-diagonal 2DCS peaks to the localized nature of the matter Majorana excitations trapped by Z_{2} flux excitations and show that 2DCS thus directly probes the inverse participation ratio of Majorana wave functions. By providing experimentally observable features of spin liquid states in the 2D spectrum, our Letter can guide future 2DCS experiments on Kitaev magnets.

Incorporating non-local anyonic statistics into a graph decomposition

In this work we describe how to systematically implement a full graph decomposition to set up a linked-cluster expansion for the topological phase of Kitaev’s toric code in a field. This demands to include the non-local effects mediated by the mutual anyonic statistics of elementary charge and flux excitations. Technically, we describe how to consistently integrate such non-local effects into a hypergraph decomposition for single excitations. The approach is demonstrated for the ground-state energy and the elementary excitation energies of charges and fluxes in the perturbed topological phase.

Investigating Advanced Building Envelopes for Energy Efficiency in Prefab Temporary Post-Disaster Housing

Prefabricated temporary buildings are a promising solution for post-disaster scenarios for their modularity, sustainability and transportation advantages. However, their low thermal mass building envelope shows a fast response to heat flux excitations. This leads to the risk of not meeting the occupant comfort and HVAC energy-saving requirements. The literature shows different measures implementable in opaque surfaces, like vacuum insulation panels (VIPs), phase change materials (PCMs) and switchable coatings, and in transparent surfaces (switchable glazing) to mitigate thermal issues, like overheating, while preserving the limited available internal space. This paper investigates the energy and overheating performance of the mentioned interventions by using building performance simulation tools to assess their effectiveness. The optimization also looks at the transportation flexibility of each intervention to better support the decision maker for manufacturing innovative temporary units. The most energy-efficient measures turn to be VIPs as a better energy solution for winter and PCMs as a better thermal comfort solution for summer.

Majorana-fermion mean field theories of Kitaev quantum spin liquids

We determine the phase diagrams of anisotropic Kitaev-Heisenberg models on the honeycomb lattice using parton mean-field theories based on different Majorana fermion representations of the S=1/2 spin operators. First, we use a two-dimensional Jordan-Wigner transformation (JWT) involving a semi-infinite snake string operator. To ensure that the fermionized Hamiltonian remains local, we consider the limit of extreme Ising exchange anisotropy in the Heisenberg sector. Second, we use the conventional Kitaev representation in terms of four Majorana fermions subject to local constraints, which we enforce through Lagrange multipliers. For both representations, we self-consistently decouple the interaction terms in the bond and magnetization channels and determine the phase diagrams as a function of the anisotropy of the Kitaev couplings and the relative strength of the Ising exchange. While both mean-field theories produce identical phase boundaries for the topological phase transition between the gapless and gapped Kitaev quantum spin liquids, the JWT fails to correctly describe the magnetic instability and finite-temperature behavior. Our results show that the magnetic phase transition is first order at low temperatures but becomes continuous above a certain temperature. At this energy scale, we also observe a finite-temperature crossover on the quantum-spin-liquid side, from a fractionalized paramagnet at low temperatures, in which gapped flux excitations are frozen out, to a conventional paramagnet at high temperatures. Published by the American Physical Society 2024

Fractionalized Prethermalization in a Driven Quantum Spin Liquid.

Quantum spin liquids subject to a periodic drive can display fascinating nonequilibrium heating behavior because of their emergent fractionalized quasiparticles. Here, we investigate a driven Kitaev honeycomb model and examine the dynamics of emergent Majorana matter and Z_{2} flux excitations. We uncover a distinct two-step heating profile-dubbed fractionalized prethermalization-and a quasistationary state with vastly different temperatures for the matter and the flux sectors. We argue that this peculiar prethermalization behavior is a consequence of fractionalization. Furthermore, we discuss an experimentally feasible protocol for preparing a zero-flux initial state of the Kiteav honeycomb model with a low energy density, which can be used to observe fractionalized prethermalization in quantum information processing platforms.

Nonlinear response of the Kitaev honeycomb lattice model in a weak magnetic field

We investigate the nonlinear response of the Kitaev honeycomb lattice model in a weak magnetic field using the theory of two-dimensional (2D) coherent spectroscopy. We observe that at the isotropic point in the non-Abelian phase of this model, the nonlinear spectrum in the 2D frequency domain consists of sharp signals that originate from the flux excitations and Majorana bound states. Signatures of different flux excitations can be clearly observed in this spectrum, such that one can observe evidences of flux states with 4-adjacent, 2-nonadjacent, and 4-far-separated fluxes, which are not visible in linear response spectroscopy such as neutron scattering experiments. Moreover, in the Abelian phase we perceive that the spectrum in the frequency domain is composed of streak signals. These signals, as in the nonlinear response of the pure Kitaev model, represent a distinct signature of itinerant Majorana fermions. However, deep in the Abelian phase whenever a Kitaev exchange coupling is much stronger than the others, the streak signals are weakened and only single sharp spots are seen in the response, which resembles the dispersionless response of the conventional toric code.

Experimental study of grain oriented electrical steel laminations under 3D magnetic flux excitation

The magnetic behavior of a lamination stack made of grain-oriented electrical steel (GOES) is investigated under non-conventional 3D magnetic flux excitations. An experimental demonstrator has been designed to study a normal orientation of the magnetic flux path, with regard to the lamination plane, combined with different in-plane orientations of the easy magnetization axis of the lamination stack. The results in terms of the magnetic flux distribution and the iron losses are presented and discussed.

Scattering phenomena for spin transport in a Kitaev spin liquid

The Kitaev model exhibits a canonical quantum spin liquid as a ground state and hosts two fractional quasiparticles, itinerant Majorana fermion and localized flux excitation. The former can carry heat and spin modulations in the quantum spin liquid, but the role of the latter remains unknown for the transport phenomena. Here, we focus on spin transport in the presence of excited fluxes and report that they yield strong interference in the propagation of the Majorana fermions, which feel gauge-like potential emergent around the fluxes. We examine the transient spin dynamics triggered by a pulsed magnetic field at an edge. In the absence of excited fluxes, the magnetic-field pulse creates the plane wave of the Majorana fermions, which flows in the quantum spin liquid. Although this wave does not accompany the change of local spin moments in bulk, it induces local moments at the side opposite to the edge under the magnetic-field pulse. We observe the spatial modulation of induced spin moments when fluxes are excited in the bulk region. This behavior is more striking than the case of lattice defects. Moreover, we find that, although the amplitude of the spatial change is almost independent of the distance between lattice defects, it is strongly enhanced by increasing the distance for the case of excited fluxes. The difference is understood from the influence on the itinerant Majorana fermions; the lattice defects change the system locally, but flux excitations alter all the transfer integrals on the string connecting them. The present results will provide another route to observing intrinsic flux excitations distinguished from extrinsic effects such as lattice defects.

Probing signatures of fractionalization in the candidate quantum spin liquid Cu2IrO3 via anomalous Raman scattering

Long-range entanglement in quantum spin liquids (QSLs) leads to novel low-energy excitations with fractionalized quantum numbers and (in two dimensions) statistics. Experimental detection and manipulation of these excitations present a challenge particularly in view of diverse candidate magnets. A promising probe of fractionalization is their coupling to phonons. Here, we present Raman scattering results for the $S=1/2$ honeycomb iridate ${\mathrm{Cu}}_{2}{\mathrm{IrO}}_{3}$, a candidate Kitaev QSL with fractionalized Majorana fermions and Ising flux excitations. We observe anomalous low-temperature frequency shift and linewidth broadening of the Raman intensities in addition to a broad magnetic continuum, both of which, as we derive, are naturally attributed to the phonon decaying into itinerant Majoranas. The dynamic Raman susceptibility marks a crossover from the QSL to a thermal paramagnet at $\ensuremath{\sim}120$ K. The phonon anomalies below this temperature demonstrate a strong phonon-Majorana coupling. These results provide evidence of spin fractionalization in ${\mathrm{Cu}}_{2}{\mathrm{IrO}}_{3}$.

Finite-momentum energy dynamics in a Kitaev magnet

We study the energy-density dynamics at finite momentum of the two-dimensional Kitaev spin-model on the honeycomb lattice. Due to fractionalization of magnetic moments, the energy relaxation occurs through mobile Majorana matter, coupled to a static $\mathbb{Z}_2$ gauge field. At finite temperatures, the $\mathbb{Z}_2$ flux excitations act as an emergent disorder, which strongly affects the energy dynamics. We show that sufficiently far above the flux proliferation temperature, but not yet in the classical regime, gauge disorder modifies the coherent low-temperature energy-density dynamics into a form which is almost diffusive, with hydrodynamic momentum scaling of a diffusion-kernel, which however remains retarded, primarily due to the presence of two distinct relaxation channels of particle-hole and particle-particle nature. Relations to thermal conductivity are clarified. Our analysis is based on complementary calculations in the low-temperature homogeneous gauge and a mean-field treatment of thermal gauge fluctuations, valid at intermediate and high temperatures.

Controlling the RKKY interaction and heat transport in a Kitaev spin liquid via Z2 flux walls

Kitaev spin liquids (KSLs) contain both itinerant Majorana fermions and localized ${\mathbb{Z}}_{2}$ flux excitations. The mobile fermions transport energy, while the fluxes hinder heat flow. By controlling the flux configuration, one can separate a KSL into different domains via ${\mathbb{Z}}_{2}$ flux walls. We show that at low temperatures, the wall significantly suppresses the Majorana-mediated Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction and blocks the heat transfer between domains.

Geometric criterion for solvability of lattice spin systems

We present a simple criterion for solvability of lattice spin systems on the basis of the graph theory and the simplicial homology. The lattice systems satisfy algebras with graphical representations. It is shown that the null spaces of adjacency matrices of the graphs provide conserved quantities of the systems. Furthermore, when the graphs belong to a class of simplicial complexes, the Hamiltonians are found to be mapped to bilinear forms of Majorana fermions, from which the full spectra of the systems are obtained. In the latter situation, we find a relation between conserved quantities and the first homology group of the graph, and the relation enables us to interpret the conserved quantities as flux excitations of the systems. The validity of our theory is confirmed in several known solvable spin systems including the 1d transverse-field Ising chain, the 2d Kitaev honeycomb model and the 3d diamond lattice model. We also present new solvable models on a 1d tri-junction, 2d and 3d fractal lattices, and the 3d cubic lattice.

Further insights into the thermodynamics of the Kitaev honeycomb model

Here we revisit the thermodynamics of the Kitaev quantum spin liquid realized on the honeycomb lattice. We address two main questions: First, we investigate whether there are observable thermodynamic signatures of the topological Majorana boundary modes of the Kitaev honeycomb model. We argue that for the time-reversal invariant case the residual low-temperature entropy is the primary thermodynamic signature of these Majorana edge modes, and verify using large-scale Monte Carlo simulations that this residual entropy is present in the full Kitaev model. When time-reversal symmetry is broken, the Majorana edge modes are potentially observable in more direct thermodynamic measurements such as the specific heat, though only at temperatures well below the bulk gap. % Second, we study the energetics, and the corresponding thermodynamic signatures, of the flux excitations in the Kitaev model. Specifically, we study the flux interactions on both cylinder and torus geometries numerically, and quantify their impact on the thermodynamics of the Kitaev spin liquid by using a polynomial fit for the average flux energy as a function of flux density and extrapolating it to the thermodynamic limit. By comparing this model to Monte Carlo simulations, we find that flux interactions have a significant quantitative impact on the shape and the position of the low-temperature peak in the specific heat.

Phonon renormalization in the Kitaev quantum spin liquid

We study the self-energy of phonons, magnetoelastically coupled to the two-dimensional Kitaev spin-model on the honeycomb lattice. Fractionalization of magnetic moments into mobile Majorana matter and a static $\mathbb{Z}_{2}$ gauge field lead to a continuum of relaxation processes comprising two channels. Thermal flux excitations, which act as an emergent disorder, strongly affect the phonon renormalization. Above the flux proliferation temperature, the dispersion of a narrow quasiparticle-hole channel is suppressed in favor of broad and only weakly momentum dependent features, covering large spectral ranges. Our analysis is based on complementary calculations in the low-temperature homogeneous gauge and a mean-field treatment of thermal gauge fluctuations, valid at intermediate and high temperatures.

Excitations in strict 2-group higher gauge models of topological phases

We consider an exactly solvable model for topological phases in (3+1) d whose input data is a strict 2-group. This model, which has a higher gauge theory interpretation, provides a lattice Hamiltonian realisation of the Yetter homotopy 2-type topological quantum field theory. The Hamiltonian yields bulk flux and charge composite excitations that are either point-like or loop-like. Applying a generalised tube algebra approach, we reveal the algebraic structure underlying these excitations and derive the irreducible modules of this algebra, which in turn classify the elementary excitations of the model. As a further application of the tube algebra approach, we demonstrate that the ground state subspace of the three-torus is described by the central subalgebra of the tube algebra for torus boundary, demonstrating the ground state degeneracy is given by the number of elementary loop-like excitations.

Large thermal Hall effect in α−RuCl3 : Evidence for heat transport by Kitaev-Heisenberg paramagnons

The honeycomb Kitaev model in a magnetic field is a source of a topological quantum spin liquid with Majorana fermions and gauge flux excitations as fractional quasiparticles. We present experimental results for the thermal Hall effect of the material $\alpha$-RuCl$_{3}$ which recently emerged as a prime candidate for realizing such physics. At temperatures above long-range magnetic ordering $T\gtrsim T_N\approx8$ K, we observe with an applied magnetic field $B$ perpendicular to the honeycomb layers a sizeable positive transversal heat conductivity $\kappa_{xy}$ which increases linearly with $B$. Upon raising the temperature, $\kappa_{xy}(T)$ increases strongly, exhibits a broad maximum at around 30 K, and eventually becomes negligible at $T\gtrsim 125$ K. Remarkably, the longitudinal heat conductivity $\kappa_{xx}(T)$ exhibits a sizeable positive thermal magnetoresistance effect. Thus, our findings provide clear-cut evidence for longitudinal and transverse magnetic heat transport and underpin the unconventional nature of the quasiparticles in the paramagnetic phase of $\alpha$-RuCl$_{3}$.

Confinement transition of ℤ2 gauge theories coupled to massless fermions: Emergent quantum chromodynamics and SO(5) symmetry

We study a model of fermions on the square lattice at half-filling coupled to an Ising gauge theory that was recently shown in Monte Carlo simulations to exhibit [Formula: see text] topological order and massless Dirac fermion excitations. On tuning parameters, a confining phase with broken symmetry (an antiferromagnet in one choice of Hamiltonian) was also established, and the transition between these phases was found to be continuous, with coincident onset of symmetry breaking and confinement. While the confinement transition in pure gauge theories is well-understood in terms of condensing magnetic flux excitations, the same transition in the presence of gapless fermions is a challenging problem owing to the statistical interactions between fermions and the condensing flux excitations. The conventional scenario then proceeds via a two-step transition, involving a symmetry-breaking transition leading to gapped fermions followed by confinement. In contrast, here, using quantum Monte Carlo simulations, we provide further evidence for a direct, continuous transition and also find numerical evidence for an enlarged [Formula: see text] symmetry rotating between antiferromagnetism and valence bond solid orders proximate to criticality. Guided by our numerical finding, we develop a field theory description of the direct transition involving an emergent nonabelian [[Formula: see text]] gauge theory and a matrix Higgs field. We contrast our results with the conventional Gross-Neveu-Yukawa transition.

Unusual Phonon Heat Transport in α-RuCl_{3}: Strong Spin-Phonon Scattering and Field-Induced Spin Gap.

The honeycomb Kitaev-Heisenberg model is a source of a quantum spin liquid with Majorana fermions and gauge flux excitations as fractional quasiparticles. Here we unveil the highly unusual low-temperature heat conductivity κ of α-RuCl_{3}, a prime candidate for realizing such physics: beyond a magnetic field of B_{c}≈7.5 T, κ increases by about one order of magnitude, both for in-plane as well as out-of-plane transport. This clarifies the unusual magnetic field dependence unambiguously to be the result of severe scattering of phonons off putative Kitaev-Heisenberg excitations in combination with a drastic field-induced change of the magnetic excitation spectrum. In particular, an unexpected, large energy gap arises, which increases linearly with the magnetic field, reaching remarkable ℏω_{0}/k_{B}≈50 K at 18T.

Reduction of Power Transformer Core Noise Generation Due to Magnetostriction-Induced Deformations Using Fully Coupled Finite-Element Modeling Optimization Procedures

This paper focuses on the development of an algorithm for the prediction of transformer core deformation, using a fully coupled magneto-mechanical approach. An imposed magnetic flux method coupled with finite-element modeling is employed for the magnetic resolution. The constitutive law of the material is considered with a simplified multi-scale model describing both magnetic and magnetostrictive anisotropies. Magnetostriction is introduced as an input free strain of a mechanical problem to get the deformation and displacement fields. A 3-D estimation of acoustic power is carried out to evaluate the global core deformation and acoustic noise level. The numerical process is applied to a three-phase transformer made of grain-oriented FeSi core, leading to a set of noise estimation for different flux excitations and core geometries.

Coherent hole propagation in an exactly solvable gapless spin liquid

We examine the dynamics of a single hole in the gapless phase of the Kitaev honeycomb model, focusing on the slow-hole regime where the bare hopping amplitude $t$ is much less than the Kitaev exchange energy $J$. In this regime, the hole does not generate gapped flux excitations and is dressed only by the gapless fermion excitations. Investigating the single-hole spectral function, we find that the hole propagates coherently with a quasiparticle weight that is finite but approaches zero as $t/J \to 0$. This conclusion follows from two approximate treatments, which capture the same physics in complementary ways. Both treatments use the stationary limit as an exactly solvable starting point to study the spectral function approximately (i) by employing a variational approach in terms of a trial state that interpolates between the limits of a stationary hole and an infinitely fast hole and (ii) by considering a special point in the gapless phase that corresponds to a simplified one-dimensional problem.