Topological states of matter such as quantum spin liquids (QSLs) are of great interest because of their remarkable predicted properties including protection of quantum information and the emergence of Majorana fermions. Such QSLs, however, have proven difficult to identify experimentally. The most promising approach is to study their exotic nature via the wavevector and intensity dependence of their dynamical response in neutron scattering. A major search has centered on iridate materials which are proposed to realize the celebrated Kitaev model on a honeycomb lattice -a prototypical topological QSL system in two dimensions (2D). The difficulties of iridium for neutron measurements have, however, impeded progress significantly. Here we provide experimental evidence that a material based on ruthenium, α-RuCl 3 realizes the same Kitaev physics but is highly amenable to neutron investigation. Our measurements confirm the requisite strong spin-orbit coupling, and a low temperature 2 magnetic order that matches the predicted phase proximate to the QSL. We also show that stacking faults, inherent to the highly 2D nature of the material, readily explain some puzzling results to date. Measurements of the dynamical response functions, especially at energies and temperatures above that where interlayer effects are manifest, are naturally accounted for in terms of deconfinement physics expected for QSLs. Via a comparison to the recently calculated dynamics from gauge flux excitations and Majorana fermions of the pure Kitaev model we propose α-RuCl 3 as the prime candidate for experimental realization of fractionalized Kitaev physics.Exotic physics associated with frustrated quantum magnets is an enduring theme in condensed matter research. The formation of quantum spin liquids (QSL) The Kitaev model consists of a set of spin-1/2 moments � ���⃗ � arrayed on a honeycomb lattice. The Kitaev couplings, of strength K in eqn.(1) are highly anisotropic with a different spin component interacting for each of the three bonds of the honeycomb lattice. In actual materials a Heisenberg interaction (J) is also generally expected to be present, giving rise to the Heisenberg-Kitaev (H-K) Hamiltonian given by 11 .where, for example, m is the component of the spin directed along the bond connecting spins (i,j). The QSL phase of the pure Kitaev model (J=0), for both ferro and antiferromagnetic K, is stable for relatively small Heisenberg perturbations.Remarkably the Hamiltonian (1) has been proposed to accurately describe octahedrallycoordinated magnetic systems, Fig. 1 21 -27 . Whilst these studies lend support to the material as a potential Kitaev material, conflicting results centering on the low temperature magnetic properties have hindered progress. To resolve this we undertake a comprehensive evaluation of the magnetic and spin orbit properties of α-RuCl 3 , and further measure the dynamical response establishing this as a material proximate to the widely searched for quantum spin liquid.We begin by investigating the crystal and m...

Topological states of matter present a wide variety of striking new phenomena. Prominent among these is the fractionalisation of electrons into unusual particles: Majorana fermions [1], Laughlin quasiparticles [2] or magnetic monopoles [3]. Their detection, however, is fundamentally complicated by the lack of any local order, such as, for example, the magnetisation in a ferromagnet. While there are now several instances of candidate topological spin liquids [4], their identification remains challenging [5]. Here, we provide a complete and exact theoretical study of the dynamical structure factor of a two-dimensional quantum spin liquid in gapless and gapped phases. We show that there are direct signatures -qualitative and quantitativeof the Majorana fermions and gauge fluxes emerging in Kitaev's honeycomb model. These include counterintuitive manifestations of quantum number fractionalisation, such as a neutron scattering response with a gap even in the presence of gapless excitations, and a sharp component despite the fractionalisation of electron spin. Our analysis identifies new varieties of the venerable X-ray edge problem and explores connections to the physics of quantum quenches.The study of spin liquids has been central to advancing our understanding of correlated phases of quantum matter ever since Anderson's proposal of the resonating valence bond (RVB) liquid state [6], which provided, via the detour of hightemperature superconductivity, an early instance of a fractionalised topological state [7,8]. More recent manifestations hold the promise of realising an architecture of quantum computing robust against decoherence [9].Investigations of such topological states are hampered by the lack of suitable approaches, with numerical methods limited to small system sizes, to models with a robust excitation gap, or ones that avoid the sign problem in quantum Monte Carlo. A benchmark is offered by the Kitaev model [1], which can be used as a representative example of an entire class of quantum spin liquids (QSL). While being a minimal model, it combines a raft of desirable features. First, it is described by a simple Hamiltonian involving only nearest-neighbor interactions on the honeycomb lattice (Fig. 1), by virtue of which it is a promising candidate for realisation in materials physics [10], or in cold atom implementations of quantum simulators [11]. Second, it harbours two distinct topological quantum spin liquid phases, with either gapless or gapped Majorana fermion excitations. Finally, its solution can be reduced to the A B z x y 1 n n 2 J x = J z = 0 J x = J y = 0 J y = J z = 0 a b

Conventionally ordered magnets possess bosonic elementary excitations, called magnons. By contrast, no magnetic insulators in more than one dimension are known whose excitations are not bosons but fermions. Theoretically, some quantum spin liquids (QSLs) [1] -new topological phases which can occur when quantum fluctuations preclude an ordered state -are known to exhibit Majorana fermions [2] as quasiparticles arising from fractionalization of spins [3]. Alas, despite much searching, their experimental observation remains elusive. Here, we show that fermionic excitations are remarkably directly evident in experimental Raman scattering data [4] across a broad energy and temperature range in the two-dimensional material α-RuCl 3 . This shows the importance of magnetic materials as hosts of Majorana fermions. In turn, this first systematic evaluation of the dynamics of a QSL at finite temperature emphasizes the role of excited states for detecting such exotic properties associated with otherwise hard-to-identify topological QSLs.The Kitaev model has recently attracted attention as a canonical example of a QSL with emergent fractionalized fermionic excitations [2,5]. The model is defined for S = 1/2 spins on a honeycomb lattice with anisotropic bond-dependent interactions, as shown in Fig. 1a [2]. Recent theoretical work -by providing access to properties of excited states -has predicted signs of Kitaev QSLs in the dynamical response at T = 0 [6,7] and in the T dependence of thermodynamic quantities [8,9]. However, the dynamical properties at finite T have remained a theoretical challenge as it is necessary to handle quantum and thermal fluctuations simultaneously. Here, by calculating dynamical correlation functions over a wide temperature range we directly identify signatures of fractionalization in available experimental inelastic light scattering data.In real materials, Kitaev-type anisotropic interactions may appear through a superexchange process between j eff = 1/2 localized moments in the presence of strong spin-orbit coupling [10]. Such a situation is believed to be realised in several materials, such as iridates A 2 IrO 3 (A=Li, Na) [11,12] and a ruthenium compound α-RuCl 3 [4,[13][14][15]. These materials show magnetic ordering at a low T (∼ 10 K), indicating that some exchange interactions coexist with the Kitaev exchange and give rise to the magnetic order instead of the QSL ground state [16][17][18][19]. Nevertheless, evidence suggests that the Kitaev interaction is predominant (several tens to hundreds of Kelvin) [15,[18][19][20][21][22], which may provide an opportunity to observe the fractional excitations in a quantum paramagnetic state above the transition temperature as a proximity effect of the QSL phase.In particular, unconventional excitations were observed by polarized Raman scattering in α-RuCl 3 [4]. In this material, Néel ordering sets in only at T c ∼ 14K, while the Kitaev interaction appears to be much larger than the Heisenberg interaction [15,22], and hence finite-temperature signatures...

The venerable phenomena of Anderson localization, along with the much more recent many-body localization, both depend crucially on the presence of disorder. The latter enters either in the form of quenched disorder in the parameters of the Hamiltonian, or through a special choice of a disordered initial state. Here we present a model with localization arising in a very simple, completely translationally invariant quantum model, with only local interactions between spins and fermions. By identifying an extensive set of conserved quantities, we show that the system generates purely dynamically its own disorder, which gives rise to localization of fermionic degrees of freedom. Our work gives an answer to a decades old question whether quenched disorder is a necessary condition for localization. It also offers new insights into the physics of many-body localization, lattice gauge theories, and quantum disentangled liquids.The study of localization phenomena -pioneered in Anderson's seminal work on the absence of diffusion in certain random lattices [1] -is receiving redoubled attention in the context of the physics of interacting systems showing manybody localization [2][3][4]. While in these systems the presence of quenched disorder plays a central role, suggestions for interaction-induced localization in disorder-free systems appeared early in the context of solid Helium [5]. However, all of these are limited to settings having inhomogeneous initial states [6,7]. Whether quenched disorder is a general precondition for localization has remained an open question. Here, we provide an explicit example to demonstrate that a disorder-free system can generate its own randomness dynamically, which leads to localization in one of its subsystems. Our model is exactly soluble, thanks to an extensive number of conserved quantities, which we identify, allowing access to the physics of the long-time limit. The model can be extended while preserving its solubility, in particular towards investigations of disorder-free localization in higher dimensions.Localization phenomena are often diagnosed, in experiment and simulation, via the dynamical response to a global quantum quench. The underlying idea is to examine if a system thermalizes, thereby losing memory of the initial state, or whether this memory persists in the long-time limit [6][7][8][9]. Some of the simple initial states used in these diagnostics exhibit density modulations, e.g., in the form of a periodic density-wave pattern, or a density imbalance, with two halves of the system separated by a 'domain wall'. The latter setup was exploited in the experimental identification of the many-body localization (MBL) transition [10]. In this experiment a complete domain-wall melting was observed in the ergodic phase, while the density imbalance remained in the localized phase at long times, showing exponential tails set by the localization length [11]. Another useful localization diagnostic, which does not require inhomogeneous initial states, is based on examining deviations ...