Electrically charged particles, such as the electron, are ubiquitous. In contrast, no elementary particles with a net magnetic charge have ever been observed, despite intensive and prolonged searches (see ref. 1 for example). We pursue an alternative strategy, namely that of realizing them not as elementary but rather as emergent particles-that is, as manifestations of the correlations present in a strongly interacting many-body system. The most prominent examples of emergent quasiparticles are the ones with fractional electric charge e/3 in quantum Hall physics. Here we propose that magnetic monopoles emerge in a class of exotic magnets known collectively as spin ice: the dipole moment of the underlying electronic degrees of freedom fractionalises into monopoles. This would account for a mysterious phase transition observed experimentally in spin ice in a magnetic field, which is a liquid-gas transition of the magnetic monopoles. These monopoles can also be detected by other means, for example, in an experiment modelled after the Stanford magnetic monopole search.

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...

We study the quantum dimer model on the triangular lattice, which is expected to describe the singlet dynamics of frustrated Heisenberg models in phases where valence bond configurations dominate their physics. We find, in contrast to the square lattice, that there is a truly short ranged resonating valence bond phase with no gapless excitations and with deconfined, gapped, spinons for a finite range of parameters. We also establish the presence of crystalline dimer phases.

Clean and interacting periodically-driven systems are believed to exhibit a single, trivial "infinitetemperature" Floquet-ergodic phase. In contrast, here we show that their disordered Floquet manybody localized counterparts can exhibit distinct ordered phases delineated by sharp transitions. Some of these are analogs of equilibrium states with broken symmetries and topological order, while others -genuinely new to the Floquet problem -are characterized by order and non-trivial periodic dynamics. We illustrate these ideas in driven spin chains with Ising symmetry.Introduction: Extending ideas from equilibrium statistical mechanics to the non-equilibrium setting is a topic of perennial interest. We consider a question in this vein: Is there a sharp notion of a phase in driven, interacting quantum systems? We find an affirmative answer for Floquet systems 1-3 whose Hamiltonians depend on time t periodically, H(t + T ) = H(t). Unlike in equilibrium statistical mechanics, disorder turns out to be an essential ingredient for stabilizing different phases; moreover, the periodic time evolution allows for the existence (and diagnosis) of phases without any counterparts in equilibrium statistical mechanics.Naively, Floquet systems hold little promise of a complex phase structure. In systems with periodic Hamiltonians, not even the basic concept of energy survives, being replaced instead with a quasi-energy defined up to arbitrary shifts of 2π/T . Indeed, interacting Floquet systems should absorb energy indefinitely from the driving field, as suggested by standard linear response reasoning wherein any nonzero frequency exhibits dissipation. This results in the system heating up to "infinite temperature", at which point all static and dynamic correlations become trivial and independent of starting state -thus exhibiting a maximally trivial form of ergodicity 4-6 . To get anything else requires a mechanism for energy localization wherein the absorption from the driving field saturates, and the long-time state of the system is sensitive to initial conditions. The current dominant belief is that translationally invariant interacting systems cannot generically exhibit such energy localization 4-6 , although there are computations that suggest otherwise 7-9 . The basic intuition is that spatially extended modes in translationally invariant systems interact with and transfer energy between each other.This can be different when disorder spatially localizes the modes, with individual modes exhibiting something like Rabi oscillations while interacting only weakly with distant modes. While the actual situation is somewhat more involved, several pieces of work 10-12 have made a convincing case for the existence of Floquet energy localization exhibiting a set of properties closely related to those exhibited by time-independent many-body localized 13 (MBL) systems 14 . In the following we show that such Floquet-MBL sys-

The Kitaev quantum spin liquid (KQSL) is an exotic emergent state of matter exhibiting Majorana fermion and gauge flux excitations. The magnetic insulator α-RuCl is thought to realize a proximate KQSL. We used neutron scattering on single crystals of α-RuCl to reconstruct dynamical correlations in energy-momentum space. We discovered highly unusual signals, including a column of scattering over a large energy interval around the Brillouin zone center, which is very stable with temperature. This finding is consistent with scattering from the Majorana excitations of a KQSL. Other, more delicate experimental features can be transparently associated with perturbations to an ideal model. Our results encourage further study of this prototypical material and may open a window into investigating emergent magnetic Majorana fermions in correlated materials.

We study the low-temperature behaviour of the classical Heisenberg antiferromagnet with nearest neighbour interactions on the pyrochlore lattice. Because of geometrical frustration, the ground state of this model has an extensive number of degrees of freedom. We show, by analysing the effects of small fluctuations around the ground-state manifold, and from the results of Monte Carlo and molecular dynamics simulations, that the system is disordered at all temperatures, T , and has a finite relaxation time, which varies as T −1 for small T .

When interactions between magnetic degrees of freedom in a lattice are incompatible with the underlying crystal geometry, exotic phenomena such as spin ice and spin liquid phases can emerge.

We report on a systematic study of two dimensional, periodic, frustrated Ising models with a quantum dynamics introduced via a transverse magnetic field. The systems studied are the triangular and kagome lattice antiferromagnets, fully frustrated models on the square and hexagonal (honeycomb) lattices, a planar analog of the pyrochlore antiferromagnet, a pentagonal lattice antiferromagnet as well as a two quasi one-dimensional lattices that have considerable pedagogical value. All of these exhibit a macroscopic degeneracy at T = 0 in the absence of the transverse field, which enters as a singular perturbation. We analyze these systems with a combination of a variational method at weak fields, a perturbative Landau-Ginzburg-Wilson (LGW) approach from large fields as well as quantum Monte Carlo simulations utilizing a cluster algorithm. Our results include instances of quantum order arising from classical criticality (triangular lattice) or classical disorder (pentagonal and probably hexagonal) as well as notable instances of quantum disorder arising from classical disorder (kagome). We also discuss the effect of a finite temperature, as well as the interplay between longitudinal and transverse fields-in the kagome problem the latter gives rise to a non-trivial phase diagram with bond-ordered and bond-critical phases in addition to the disordered phase. We also note connections to quantum dimer models and thereby to the physics of Heisenberg antiferromagnets in short-ranged resonating valence bond phases that have been invoked in discussions of high-temperature superconductivity.