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Band structures are ubiquitous in condensed matter physics and their symmetries constrain possible degeneracies, topology and response functions across a broad range of different systems. Here we address the question: given a parent crystal, what is the symmetry of hopping models on that lattice at a given shell number? We find that the parent structure does not, in general, determine the symmetry of the tight-binding model. Instead, the symmetry is dependent on the hopping range. The key to symmetry breakdown on the lattice is the existence of different {\it bond equivalence classes} whose number is related to group-subgroup indices for a broad classes of cases. We find all bond equivalence classes for $s$-wave hopping out to 20th neighbor across the different space groups and Wyckoff positions and the symmetries of the associated tight-binding models. These observations naturally lead to the definition of a {\it bond complex} $-$ the possible classes of networks of bonds to which symmetries may be enhanced from a given parent structure., Comment: 84 pages (24 pages text followed by tables), 14 figures

The insulating magnetic pyrochlore Ce$_2$Zr$_2$O$_7$ has attracted much attention as a quantum spin ice candidate with dipole-octupole character that permits spin ice phases based not only on magnetic dipole moments but also allows for even-more-exotic octupole-based spin ice phases. This work reports low-temperature neutron diffraction measurements on single crystal Ce$_2$Zr$_2$O$_7$ with $Q$-coverage both at low $Q$ where the magnetic form factor for dipoles is near maximal and at high $Q$ covering the region where the magnetic form factor for Ce$^{3+}$ octupoles is near maximal. This study was motivated by recent powder neutron diffraction studies of other Ce-based dipole-octupole pyrochlores, Ce$_2$Sn$_2$O$_7$ and Ce$_2$Hf$_2$O$_7$, which each showed temperature-dependent diffuse diffraction at high $Q$ that was interpreted as arising from octupolar correlations. Our measurements use an optimized single crystal diffuse scattering instrument that allows us to screen against strong single crystal Bragg scattering in Ce$_2$Zr$_2$O$_7$. The temperature-difference neutron diffraction reveals a low-$Q$ peak consistent with dipolar spin ice correlations. For larger $Q$, the temperature-difference neutron diffraction shows an alternation between positive and negative net intensity. These features are qualitatively consistent with the corresponding numerical-linked-cluster (NLC) calculations using pseudospin interaction parameters reported for Ce$_2$Zr$_2$O$_7$, Ce$_2$Sn$_2$O$_7$, or Ce$_2$Hf$_2$O$_7$. Importantly, neither the measured data nor any of the NLC calculations show increased scattering at high $Q$ resulting from octupolar correlations. We conclude that at the lowest attainable temperatures for our measurement ($T = 0.05$ K), octupolar correlations are not present in Ce$_2$Zr$_2$O$_7$ on the level of our observation threshold of $\sim$ 0.1$\%$ of the low-$Q$ dipole scattering.

We report the experimental discovery of orbital vortex lines in the three-dimensional (3D) band structure of a topological semimetal. Combining linear and circular dichroism in soft x-ray angle-resolved photoemission (SX-ARPES) with first-principles theory, we image the winding of atomic orbital angular momentum, thereby revealing - and determining the location of - lines of vorticity in full 3D momentum space. Our observation of momentum-space vortex lines with quantized winding number establishes an analogue to real-space quantum vortices, for instance, in type-II superconductors and certain non-collinear magnets. These results establish multimodal dichroism in SX-ARPES as an approach to trace 3D orbital textures. Our present findings particularly constitute the first imaging of non-trivial quantum-phase winding at line nodes and may pave the way to new orbitronic phenomena in quantum materials

We report new heat capacity measurements on single crystal Ce$_2$Zr$_2$O$_7$ down to $\sim$ 0.1 K in a magnetic field along the $[1,\bar{1}, 0]$ direction. These new measurements show that the broad hump in the zero-field heat capacity moves higher in temperature with increasing field strength and is split into two humps by the $[1,\bar{1}, 0]$ field at $\sim$ 2 T. These separate features are due to the decomposition of the pyrochlore lattice into effectively decoupled chains for fields in this direction: one set of chains ($\alpha$-chains) is polarized by the field while the other ($\beta$-chains) remains free. Our theoretical modelling suggests that the $\beta$-chains are close to a critical state, with nearly-gapless excitations. We also report new elastic and inelastic neutron scattering measurements on single crystal Ce$_2$Zr$_2$O$_7$ in $[1, \bar{1}, 0]$ and $[0, 0, 1]$ magnetic fields at temperatures down to 0.03 K. The elastic scattering behaves consistently with the formation of independent chains for a $[1, \bar{1}, 0]$ field, while the $[0, 0, 1]$ field produces a single field-induced magnetic Bragg peak at $(0, 2, 0)$ and equivalent wavevectors, indicating a polarized spin ice for fields above $\sim$ 3 T. For both $[1, \bar{1}, 0]$ and $[0, 0, 1]$ fields, our inelastic neutron scattering results show an approximately-dispersionless continuum of scattering that increases in both energy and intensity with increasing field strength. By modelling the complete set of experimental data using numerical linked cluster and semiclassical molecular dynamics calculations, we demonstrate the dominantly multipolar nature of the exchange interactions in Ce$_2$Zr$_2$O$_7$ and the smallness of the parameter $\theta$ which controls the mixing between dipolar and octupolar degrees of freedom. These results support previous estimates of the microscopic exchange parameters.

We analyse the near-adiabatic dynamics in a ramp through the critical point (CP) of the classical transverse field Ising chain. This is motivated, conceptually, by the fact that this CP -- unlike its quantum counterpart -- experiences no thermal or quantum fluctuations, and technically by the tractability of its effective model. For a `half-ramp' from ferromagnet to CP, the longitudinal and transverse magnetization scale as $\tau^{-1/3}$ and $\tau^{-2/3}$, respectively, with $1/\tau$ the ramp rate, in accord with Kibble-Zurek theory. For ferro- to paramagnetic ramps across the CP, however, they stay closer, $\tau^{-1/2}$ and $\tau^{-1}$, to adiabaticity. This adiabaticity enhancement compared to the half ramp is understood by casting the dynamics in the paramagnet in the form of a non-hermitian Dirac Hamiltonian, with the CP playing the role of an exceptional point, opening an additional decay channel., Comment: 6 pages, 3 figures

The dipolar-octupolar (DO) pyrochlores, R$_2$M$_2$O$_7$ (R = Ce, Sm, Nd), are key players in the search for realizable novel quantum spin liquid (QSL) states as a large parameter space within the DO pyrochlore phase diagram is theorized to host QSL states of both dipolar and octupolar nature. New single crystals and powders of Ce$_2$Sn$_2$O$_7$, synthesized by hydrothermal techniques, present an opportunity for a new characterization of the exchange parameters in Ce$_2$Sn$_2$O$_7$ using the near-neighbor $XYZ$ model Hamiltonian associated with DO pyrochlores. Utilizing quantum numerical linked cluster expansion fits to heat capacity and magnetic susceptibility measurements, and classical Monte Carlo calculations to the diffuse neutron diffraction of the new hydrothermally grown Ce$_2$Sn$_2$O$_7$ samples, we place Ce$_2$Sn$_2$O$_7$'s ground state within the ordered dipolar all-in-all-out (AIAO) N\'{e}el phase, with quantum Monte Carlo calculations showing a transition to long-range order at temperatures below those accessed experimentally. Indeed, our new neutron diffraction measurements on the hydrothermally grown Ce$_2$Sn$_2$O$_7$ powders show a broad signal at low scattering wave vectors, reminiscent of a \textit{dipolar} spin ice, in striking contrast from previous powder neutron diffraction on samples grown from solid-state synthesis, which found diffuse scattering at high scattering wave vectors associated with magnetic {\it octupoles} and suggested an octupolar quantum spin ice state. We conclude that new hydrothermally grown Ce$_2$Sn$_2$O$_7$ samples host a finite-temperature proximate dipolar spin ice phase, above the expected transition to AIAO N\'{e}el order., Comment: 16 pages, 12 figures

We report the manifestation of field-induced Berezinskii-Kosterlitz-Thouless (BKT) correlations in the weakly coupled spin-1/2 Heisenberg layers of the molecular-based bulk material [Cu(pz)$_2$(2-HOpy)$_2$](PF$_6$)$_2$. Due to the moderate intralayer exchange coupling of $J/k_\mathrm{B} = 6.8$ K, the application of laboratory magnetic fields induces a substantial $XY$ anisotropy of the spin correlations. Crucially, this provides a significant BKT regime, as the tiny interlayer exchange $J^\prime / k_\mathrm{B} \approx 1$ mK only induces 3D correlations upon close approach to the BKT transition with its exponential growth in the spin-correlation length. We employ nuclear magnetic resonance and $\mu^{+}$SR measurements to probe the spin correlations that determine the critical temperatures of the BKT transition as well as that of the onset of long-range order. Further, we perform stochastic series expansion quantum Monte Carlo simulations based on the experimentally determined model parameters. Finite-size scaling of the in-plane spin stiffness yields excellent agreement of critical temperatures between theory and experiment, providing clear evidence that the nonmonotonic magnetic phase diagram of [Cu(pz)$_2$(2-HOpy)$_2$](PF$_6$)$_2$ is determined by the field-tuned $XY$ anisotropy and the concomitant BKT physics., Comment: 10 pages, 7 figures

We present a theory of optimal topological textures in nonlinear sigma-models with degrees of freedom living in the Grassmannian $\mathrm{Gr}(M,N)$ manifold. These textures describe skyrmion lattices of $N$-component fermions in a quantising magnetic field, relevant to the physics of graphene, bilayer and other multicomponent quantum Hall systems near integer filling factors $\nu>1$. We derive analytically the optimality condition, minimizing topological charge density fluctuations, for a general Grassmannian sigma model $\mathrm{Gr}(M,N)$ on a sphere and a torus, together with counting arguments which show that for any filling factor and number of components there is a critical value of topological charge $d_c$ above which there are no optimal textures. Below $d_c$ a solution of the optimality condition on a torus is unique, while in the case of a sphere one has, in general, a continuum of solutions corresponding to new {\it non-Goldstone} zero modes, whose degeneracy is not lifted (via a order from disorder mechanism) by any fermion interactions depending only on the distance on a sphere. We supplement our general theoretical considerations with the exact analytical results for the case of $\mathrm{Gr}(2,4)$, appropriate for recent experiments in graphene., Comment: 15 pages, 2 figures

We study single crystals of Dy$_2$Ti$_2$O$_7$ and Ho$_2$Ti$_2$O$_7$ under magnetic field and stress applied along their [001] direction. We find that many of the features that the emergent gauge field of spin ice confers to the macroscopic magnetic properties are preserved in spite of the finite temperature. The magnetisation vs. field shows an upward convexity within a broad range of fields, while the static and dynamic susceptibilities present a peculiar peak. Following this feature for both compounds, we determine a single experimental transition curve: that for the Kasteleyn transition in three dimensions, proposed more than a decade ago. Additionally, we observe that compression up to $-0.8\%$ along [001] does not significantly change the thermodynamics. However, the dynamical response of Ho$_2$Ti$_2$O$_7$ is quite sensitive to changes introduced in the ${\rm Ho}^{3+}$ environment. Uniaxial compression can thus open up experimental access to equilibrium properties of spin ice at low temperatures.

Band topology is both constrained and enriched by the presence of symmetry. The importance of anti-unitary symmetries such as time reversal was recognized early on leading to the classification of topological band structures based on the ten-fold way. Since then, lattice point group and non-symmorphic symmetries have been seen to lead to a vast range of possible topologically nontrivial band structures many of which are realized in materials. In this paper we show that band topology is further enriched in many physically realizable instances where magnetic and lattice degrees of freedom are wholly or partially decoupled. The appropriate symmetry groups to describe general magnetic systems are the spin-space groups. Here we describe cases where spin-space groups are essential to understand the band topology in magnetic materials. We then focus on magnon band topology where the theory of spin-space groups has its simplest realization. We consider magnetic Hamiltonians with various types of coupling including Heisenberg and Kitaev couplings revealing a hierarchy of enhanced magnetic symmetry groups depending on the nature of the lattice and the couplings. We describe, in detail, the associated representation theory and compatibility relations thus characterizing symmetry-enforced constraints on the magnon bands revealing a proliferation of nodal points, lines, planes and volumes., Comment: 30 pages, 7 figures

Inspired by recent developments in the study of chaos in many-body systems, we construct a measure of local information spreading for a stochastic Cellular Automaton in the form of a spatiotemporally resolved Hamming distance. This decorrelator is a classical version of an Out-of-Time-Order Correlator studied in the context of quantum many-body systems. Focusing on the one-dimensional Kauffman Cellular Automaton, we extract the scaling form of our decorrelator with an associated butterfly velocity $v_b$ and a velocity-dependent Lyapunov exponent $\lambda(v)$. The existence of the latter is not a given in a discrete classical system. Second, we account for the behaviour of the decorrelator in a framework based solely on the boundary of the information spreading, including an effective boundary random walk model yielding the full functional form of the decorrelator. In particular, we obtain analytic results for $v_b$ and the exponent $\beta$ in the scaling ansatz $\lambda(v) \sim \mu (v - v_b)^\beta$, which is usually only obtained numerically. Finally, a full scaling collapse establishes the decorrelator as a unifying diagnostic of information spreading., Comment: 5+1 pages, 4 figures

We exhibit an exactly solvable example of a SU(2) symmetric Majorana spin liquid phase, in which quenched disorder leads to random-singlet phenomenology. More precisely, we argue that a strong-disorder fixed point controls the low temperature susceptibility $\chi(T)$ of an exactly solvable $S=1/2$ model on the decorated honeycomb lattice with quenched bond disorder and/or vacancies, leading to $\chi(T) = {\mathcal C}/T+ {\mathcal D} T^{\alpha(T) - 1}$ where $\alpha(T) \rightarrow 0$ as $T \rightarrow 0$. The first term is a Curie tail that represents the emergent response of vacancy-induced spin textures spread over many unit cells: it is an intrinsic feature of the site-diluted system, rather than an extraneous effect arising from isolated free spins. The second term, common to both vacancy and bond disorder (with different $\alpha(T)$ in the two cases) is the response of a random singlet phase, familiar from random antiferromagnetic spin chains and the analogous regime in phosphorus-doped silicon (Si:P)., Comment: two-column format; 4+pages; 3 figures

Quantum spin liquids are long-range entangled states of matter with emergent gauge fields and fractionalized excitations. While candidate materials, such as the Kitaev honeycomb ruthenate $\alpha$-RuCl$_3$, show magnetic order at low temperatures $T$, here we demonstrate numerically a dynamical crossover from magnon-like behavior at low $T$ and frequencies $\omega$ to long-lived fractionalized fermionic quasiparticles at higher $T$ and $\omega$. This crossover is akin to the presence of spinon continua in quasi-1D spin chains. It is further shown to go hand in hand with persistent typicality down to very low $T$. This aspect, which has also been observed in the spin-1/2 kagome Heisenberg antiferromagnet, is a signature of proximate spin liquidity and emergent gauge degrees of freedom more generally, and can be the basis for the numerical study of many finite-$T$ properties of putative spin liquids., Comment: 13 pages, 11 figures, accepted version

A nearly free electron metal and a Mott insulating state can be thought of as opposite ends of possibilities for the motion of electrons in a solid. In the magnetic oxide metal PdCrO$_{2}$, these two coexist as alternating layers. Using angle resolved photoemission, we surprisingly find sharp band-like features in the one-electron removal spectral function of the correlated subsystem. We show that these arise because a hole created in the Mott layer moves to and propagates in the metallic layer while retaining memory of the Mott layer's magnetism. This picture is quantitatively supported by a strong coupling analysis capturing the physics of PdCrO$_{2}$ in terms of a Kondo lattice Hamiltonian. Our findings open new routes to use the non-magnetic probe of photoemission to gain insights into the spin-susceptibility of correlated electron systems.

We study the role of zero-point quantum fluctuations in a range of magnetic states which on the classical level are close to spin-aligned ferromagnets. These include Skyrmion textures characterized by non-zero topological charge, and topologically-trivial spirals arising from the competition of the Heisenberg and Dzyaloshinskii-Moriya interactions. For the former, we extend our previous results on quantum exactness of classical Bogomolny-Prasad-Sommerfield (BPS) ground-state degeneracies to the general case of K\"ahler manifolds, with a specific example of Grassmann manifolds $\mathrm{Gr(M,N)}$. These are relevant to quantum Hall ferromagnets with $\mathrm{N}$ internal states and integer filling factor $\mathrm{M}$. A promising candidate for their experimental implementation is monolayer graphene with $\mathrm{N=4}$ corresponding to spin and valley degrees of freedom at the charge neutrality point with $\mathrm{M=2}$ filled Landau levels. We find that the vanishing of the zero-point fluctuations in taking the continuum limit occurs differently in the case of BPS states compared to the case of more general smooth textures, with the latter exhibiting more pronounced lattice effects. This motivates us to consider the vanishing of zero-point fluctuations in such near-ferromagnets more generally. We present a family of lattice spin models for which the vanishing of zero-point fluctuations is evident, and show that some spirals can be thought of as having nonzero but weak zero-point fluctuations on account of their closeness to this family. Between them, these instances provide concrete illustrations of how the Casimir energy, dependent on the full UV-structure of the theory, evolves as the continuum limit is taken., Comment: 12 pages, 8 figures

We consider spinless fermions on a finite one-dimensional lattice, interacting via nearest-neighbor repulsion and subject to a strong electric field. In the non-interacting case, due to Wannier-Stark localization, the single-particle wave functions are exponentially localized even though the model has no quenched disorder. We show that this system remains localized in the presence of interactions and exhibits physics analogous to models of conventional many-body localization (MBL). In particular, the entanglement entropy grows logarithmically with time after a quench, albeit with a slightly different functional form from the MBL case, and the level statistics of the many-body energy spectrum are Poissonian. We moreover predict that a quench experiment starting from a charge-density wave state would show results similar to those of Schreiber et al. [Science 349, 842 (2015)]., Comment: 8 pages, 7 figures, including Supplemental Material. Typo in expression for W_j fixed, and a few other small errors corrected

Magnetic remanence - found in bar magnets or magnetic storage devices - is probably the oldest and most ubiquitous phenomenon underpinning technological applications of magnetism. It is a macroscopic non-equilibrium phenomenon: a remanent magnetisation appears when a magnetic field is applied to an initially unmagnetised ferromagnet, and then taken away. Here, we present an inverted magnetic hysteresis loop in the pyrochlore compound Nd$_2$Hf$_2$O$_7$: the remanent magnetisation points in a direction opposite to the applied field. This phenomenon is exquisitely tunable as a function of the protocol in field and temperature, and it is reproducible as in a quasi-equilibrium setting. We account for this phenomenon in considerable detail in terms of the properties of non-equilibrium population of domain walls which exhibit a magnetic moment between domains of an ordered antiferromagnetic state which itself has zero net magnetisation. Properties and (non-equilibrium) dynamics of topological defects play an important role in modern spintronics, and our study adds an instance where a uniform field couples selectively to domain walls rather than the bulk., Comment: 5 pages, 3 figures in main article and 7 pages, 13 figures in supplementary materials

We study the Kitaev-Heisenberg-$\Gamma$-$\Gamma'$ model that describes the magnetism in strong spin-orbit coupled honeycomb lattice Mott insulators. In strong $[111]$ magnetic fields that bring the system into the fully polarized paramagnetic phase, we find that the spin wave bands carry nontrivial Chern numbers over large regions of the phase diagram implying the presence of chiral magnon edge states. In contrast to other topological magnon systems, the topological nontriviality of these systems results from the presence of magnon number non-conserving terms in the Hamiltonian. Since the effects of interactions are suppressed by $J/h$, the validity of the single particle picture is tunable making paramagnetic phases particularly suitable for the exploration of this physics. Using time dependent DMRG and interacting spin wave theory, we demonstrate the presence of the chiral edge mode and its evolution with field., Comment: 16 pages (main text + supplementary material), 10 figures

We study the inelastic neutron scattering cross section in the vicinity of touching points in magnon bands. Among the possible touching points are magnon Weyl points in three dimensional ordered magnets with significant spin-orbit coupling that are characterized by a linear dispersion in their vicinity. A Weyl point is topologically protected by its net chirality and here we show that this leads to a characteristic form for the dynamical structure factor. To address this question, we show that scattering intensities in the vicinity of arbitrary magnon two-band touching points are identical to expectation values of the pseudospin polarization along some direction $\hat{\boldsymbol{n}}$ in momentum space fixed by the magnetic Hamiltonian. This approach applied to Weyl points shows that they are singular points in the intensity of the form $\hat{\boldsymbol{n}}\cdot \delta\hat{\boldsymbol{k}}$ regardless of the magnetic ground state. We make specific predictions for the experimental signatures of such intensity singularities in several spin models hosting Weyl magnons applicable to candidate materials., Comment: 5 pages, 3 figures

Motivated by current interest in the dynamics of trapped quantum gases, we study the microcanonical dynamics of a trapped one-dimensional gas of classical particles interacting via a finite-range repulsive force of tunable strength. We examine two questions which have been of interest in quantum dynamics: (1) the breathing mode (size oscillation) dynamics of the trapped gas and the dependence of the breathing frequency on the interaction strength, and (2) the long-time relaxation and possible thermalization of the finite isolated gas. We show that the breathing mode frequency has non-monotonic dependence on the magnitude of the mutual repulsion, decreasing for small interactions and increasing for larger interactions. We explain these dependences in terms of slowing-down or speeding-up effects of two-body collision processes. We find that the gas thermalizes within a reasonable finite timescale in the sense of single-particle energies acquiring a Boltzmann distribution, only when the interaction strength is large compared to the energy per particle., Comment: 19 pages, 12 figures

The Kitaev model on a honeycomb lattice predicts a paradigmatic quantum spin liquid (QSL) exhibiting Majorana Fermion excitations. The insight that Kitaev physics might be realized in practice has stimulated investigations of candidate materials, recently including alpha-RuCl3. In all the systems studied to date, non-Kitaev interactions induce magnetic order at low temperature. However, in-plane magnetic fields of roughly 8 Tesla suppress the long-range magnetic order in alpha-RuCl3 raising the intriguing possibility of a field-induced QSL exhibiting non-Abelian quasiparticle excitations. Here we present inelastic neutron scattering in alpha-RuCl3 in an applied magnetic field. At a field of 8 Tesla, the spin waves characteristic of the ordered state vanish throughout the Brillouin zone. The remaining single dominant feature of the response is a broad continuum centered at the Gamma point, previously identified as a signature of fractionalized excitations. This provides compelling evidence that a field-induced QSL state has been achieved., Comment: 32 pages, 7 figures

The solution space of many classical optimization problems breaks up into clusters which are extensively distant from one another in the Hamming metric. Here, we show that an analogous quantum clustering phenomenon takes place in the ground state subspace of a certain quantum optimization problem. This involves extending the notion of clustering to Hilbert space, where the classical Hamming distance is not immediately useful. Quantum clusters correspond to macroscopically distinct subspaces of the full quantum ground state space which grow with the system size. We explicitly demonstrate that such clusters arise in the solution space of random quantum satisfiability (3-QSAT) at its satisfiability transition. We estimate both the number of these clusters and their internal entropy. The former are given by the number of hardcore dimer coverings of the core of the interaction graph, while the latter is related to the underconstrained degrees of freedom not touched by the dimers. We additionally provide new numerical evidence suggesting that the 3-QSAT satisfiability transition may coincide with the product satisfiability transition, which would imply the absence of an intermediate entangled satisfiable phase., Comment: 11 pages, 6 figures

Equilibrium theormodynamics is characterized by two fundamental ideas: thermalisation--that systems approach a late time thermal state; and phase structure--that thermal states exhibit singular changes as various parameters characterizing the system are changed. We summarise recent progress that has established generalizations of these ideas to periodically driven, or Floquet, closed quantum systems. This has resulted in the discovery of entirely new phases which exist only out of equilibrium, such as the $\pi$-spin glass or Floquet time crystal., Comment: short (6 pages) pedagogical introduction to recent developments, 2 figures

Weyl semimetals are gapless three-dimensional topological materials where two bands touch at an even number of points in the bulk Brillouin zone. These semimetals exhibit topologically protected surface Fermi arcs, which pairwise connect the projected bulk band touchings in the surface Brillouin zone. Here, we analyze the quasiparticle interference patterns of the Weyl phase when time-reversal symmetry is explicitly broken. We use a multi-band $d$-electron Hubbard Hamiltonian on a pyrochlore lattice, relevant for the pyrochlore iridate R$_2$Ir$_2$O$_7$ (where R is a rare earth). Using exact diagonalization, we compute the surface spectrum and quasiparticle interference (QPI) patterns for various surface terminations and impurities. We show that the spin and orbital texture of the surface states can be inferred from the absence of certain backscattering processes and from the symmetries of the QPI features for non-magnetic and magnetic impurities. Furthermore, we show that the QPI patterns of the Weyl phase in pyrochlore iridates may exhibit additional interesting features that go beyond those found previously in TaAs., Comment: 15 pages, 16 figures

Quantum spin systems are by now known to exhibit a large number of different classes of spin liquid phases. By contrast, for \textit{classical} Heisenberg models, only one kind of fractionalised spin liquid phase, the so-called Coulomb or $U(1)$ spin liquid, has until recently been identified: this exhibits algebraic spin correlations and impurity moments, `orphan spins', whose size is a fraction of that of the underlying microscopic degrees of freedom. Here, we present two Heisenberg models exhibiting fractionalisation in combination with exponentially decaying correlations. These can be thought of as a classical continuous spin version of a $\mathbb{Z}_2$ spin liquid. Our work suggests a systematic search and classification of classical spin liquids as a worthwhile endeavour., Comment: 5 pages, 7 figures

We study spin glass behavior in a random Ising Coulomb antiferromagnet in two and three dimensions using Monte Carlo simulations. In two dimensions, we find a transition at zero temperature with critical exponents consistent with those of the Edwards Anderson model, though with large uncertainties. In three dimensions, evidence for a finite-temperature transition, as occurs in the Edwards-Anderson model, is rather weak. This may indicate that the sizes are too small to probe the asymptotic critical behavior, or possibly that the universality class is different from that of the Edwards-Anderson model and has a lower critical dimension equal to three., Comment: 7 pages, 9 figures

The formulation of a complete theory of classical electromagnetism by Maxwell is one of the milestones of science. The capacity of many-body systems to provide emergent mini-universes with vacua quite distinct from the one we inhabit was only recognised much later. Here, we provide an account of how simple systems of localised spins manage to emulate Maxwell electromagnetism in their low-energy behaviour. They are much less constrained by symmetry considerations than the relativistically invariant electromagnetic vacuum, as their substrate provides a non-relativistic background with even translational invariance broken. They can exhibit rich behaviour not encountered in conventional electromagnetism. This includes the existence of magnetic monopole excitations arising from fractionalisation of magnetic dipoles; as well as the capacity of disorder, by generating defects on the lattice scale, to produce novel physics, as exemplified by topological spin glassiness or random Coulomb magnetism., Comment: Talk at Royal Society Symposium, "Unifying Physics and Technology in the Light of Maxwell's Equations", November 2015

We analyse the dynamical response of a range of 3D Kitaev quantum spin-liquids, using lattice models chosen to explore the different possible low-energy spectra for gapless Majorana fermions, with either Fermi surfaces, nodal lines or Weyl points. We find that the behaviour of the dynamical structure factor is distinct in all three cases, reflecting the quasiparticle density of states in two fundamentally different ways. First, the low-energy response is either straightforwardly related to the power with which the low-energy density of states vanishes; or for a non-vanishing density of states, to the phase shifts encountered in the corresponding X-ray edge problem, whose phenomenology we extend to the case of Majorana fermions. Second, at higher energies, there is a rich fine-structure, determined by microscopic features of the Majorana spectrum. Our theoretical results test the usefulness of inelastic neutron scattering as a probe of these quantum spin liquids: we find that although spin flips fractionalise, the main features of the dynamical spin response nevertheless admit straightforward interpretations in terms of Majorana and flux loop excitations., Comment: 14 pages, 9 figures

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) -- new topological phases which can occur when quantum fluctuations preclude an ordered state -- are known to exhibit Majorana fermions as quasiparticles arising from fractionalization of spins. Alas, despite much searching, their experimental observation remains elusive. Here, we show that fermionic excitations are remarkably directly evident in experimental Raman scattering data across a broad energy and temperature range in the two-dimensional material $\alpha$-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., Comment: 5 pages, 3 figures

We identify a large family of ground states of a topological Skyrmion magnet whose classical degeneracy persists to all orders in a semiclassical expansion. This goes along with an exceptional robustness of the concomitant ground state configurations, which are not at all dressed by quantum fluctuations. We trace these twin observations back to a common root: this class of topological ground states saturates a Bogomolny inequality. A similar phenomenology occurs in high-energy physics for some field theories exhibiting supersymmetry. We propose quantum Hall ferromagnets, where these Skyrmions configurations arise naturally as ground states away from integer filling, as the best available laboratory realisations., Comment: 9.5 pages

We study the effect of adding disorder to the exactly solvable Kitaev model on the hyper-honeycomb lattice, which hosts both gapped and gapless spin liquid phases with an emergent $\mathbb{Z}_2$ gauge field. The latter has an unusual gapless spectrum of Majorana fermion excitations, with a co-dimension-two Fermi ring. We thus address the question of the interplay of topological physics and disorder by considering the properties of isolated single and pair of vacancies. We show that near the vacancies, the local magnetic response to a field $h_z$ is parametrically enhanced in comparison to the pristine bulk. Unlike the previously studied case of the 2D honeycomb Kitaev model, the vacancies do not bind a flux of the $\mathbb{Z}_2$ gauge field. In the gapped phase, an isolated vacancy gives rise to effectively free spin-half moments with a non-universal coupling to an external field. In the gapless phase, the low-field magnetization is suppressed parametrically, to $(-\ln h_z)^{-1/2}$ because of interactions with the surrounding spin-liquid. We also show that a pair of vacancies is subject to a sublattice-dependent interaction on account of coupling through the bulk spin liquid, which is spatially anisotropic even when all Kitaev couplings have equal strength. This coupling is thus exponentially suppressed with distance in the gapped phase. In the gapless phase, two vacancies on the same (opposite) sublattice exhibit an enhanced (suppressed) low-field response, amounting to an effectively (anti-)ferromagnetic interaction.

Using $\rm Er_2Ti_2O_7$ as a motivation, we investigate finite-field properties of $XY$ pyrochlore antiferromagnets. In addition to a fluctuation-induced six-fold anisotropy present in zero field, an external magnetic field induces a combination of two-, three-, and six-fold clock terms as a function of its orientation providing for a rich and controllable magnetothermodynamics. For $\rm Er_2Ti_2O_7$, we predict a new phase transition for ${\bf H}\parallel [001]$. Re-entrant transitions are also found for ${\bf H}\parallel [111]$. We extend these results to the whole family the $XY$ pyrochlore antiferromagnets and show that presence and number of low-field transitions for different orientations can be used for locating a given material in the parameter space of anisotropic pyrochlores. Finite-temperature classical Monte Carlo simulations serve to confirm and illustrate these analytic predictions., Comment: 11 pages, accepted version with supplemental material

We show that the honeycomb Heisenberg antiferromagnet with $J_1/2=J_2=J_3$, where $J_{1/2/3}$ are first-, second- and third-neighbour couplings respectively, forms a classical spin liquid with pinch-point singularities in the structure factor at the Brillouin zone corners. Upon dilution with non-magnetic ions, fractionalised degrees of freedom carrying $1/3$ of the free moment emerge. Their effective description in the limit of low-temperature is that of spins randomly located on a triangular lattice, with a frustrated interaction of long-ranged logarithmic form. The XY version of this magnet exhibits nematic thermal order by disorder, which comes with a clear experimental diagnostic., Comment: 5 pages, 4 figures

While the existence of a chiral spin liquid (CSL) on a class of spin-1/2 kagome antiferromagnets is by now well-established numerically, a controlled theoretical path from the lattice model leading to a low energy topological field theory is still lacking. This we provide via an explicit construction, starting from reformulating a microscopic model for a CSL as a lattice gauge theory, and deriving the low-energy form of its continuum limit. A crucial ingredient is the realisation that the bosonic spinons of the gauge theory exhibit a $U(1)$ symmetry-protected topological (SPT) phase, which upon promoting its $U(1)$ global symmetry to a local gauge structure ("gauging") yields the CSL. We suggest that such an explicit lattice-based construction involving gauging of an SPT phase can be applied more generally to understand topological spin liquids., Comment: 5+3 pages, 3+4 figures

Motivated by recent synthesis of the hyper-honeycomb material $\beta$-$\mathrm{Li_2 Ir O_3}$, we study the dynamical structure factor (DSF) of the corresponding 3D Kitaev quantum spin-liquid (QSL), whose fractionalised degrees of freedom are Majorana fermions and emergent flux-loops. Properties of this 3D model are known to differ in important ways from those of its 2D counterpart -- it has finite-temperature phase transition, as well as distinct features in Raman response. We show, however, that the qualitative behaviour of the DSF is broadly dimension-independent. Characteristics of the 3D DSF include a response gap even in the gapless QSL phase and an energy dependence deriving from the Majorana fermion density of states. Since the majority of the response is from states containing a single Majorana excitation, our results suggest inelastic neutron scattering as the spectroscopy of choice to illuminate the physics of Majorana fermions in Kitaev QSLs., Comment: 5 pages, 5 figures

We report on measurements of the sound velocity and attenuation in a single crystal of the candidate quantum- spin-ice material Yb$_2$Ti$_2$O$_7$ as a function of temperature and magnetic field. The acoustic modes couple to the spins magneto-elastically and, hence, carry information about the spin correlations that sheds light on the intricate magnetic phase diagram of Yb$_2$Ti$_2$O$_7$ and the nature of spin dynamics in the material. Particularly, we find a pronounced thermal hysteresis in the acoustic data with a concomitant peak in the specific heat indicating a possible first-order phase transition at about $0.17$ K. At low temperatures, the acoustic response to magnetic field saturates hinting at the development of magnetic order. Furthermore, mean-field calculations suggest that Yb$_2$Ti$_2$O$_7$ undergoes a first-order phase transition from a cooperative paramagnetic phase to a ferromagnet below $T\approx 0.17$ K., Comment: 8 pages

We present the theory of dynamical spin-response for the Kitaev honeycomb model, obtaining exact results for the structure factor (SF) in gapped and gapless, Abelian and non-Abelian quantum spin-liquid (QSL) phases. We also describe the advances in methodology necessary to compute these results. The structure factor shows signatures of spin-fractionalization into emergent quasiparticles -- Majorana fermions and fluxes of $Z_2$ gauge field. In addition to a broad continuum from spin-fractionalization, we find sharp ($\delta$-function) features in the response. These arise in two distinct ways: from excited states containing only (static) fluxes and no (mobile) fermions; and from excited states in which fermions are bound to fluxes. The SF is markedly different in Abelian and non-Abelian QSLs, and bound fermion-flux composites appear only in the non-Abelian phase., Comment: 21 pages, 14 figures

We study a bosonic model with correlated hopping on a honeycomb lattice, and show that its ground state is a bosonic integer quantum Hall (BIQH) phase, a prominent example of a symmetry protected topological (SPT) phase. By using the infinite density matrix renormalization group method, we establish the existence of the BIQH phase by providing clear numerical evidence: (i) a quantized Hall conductance with $|\sigma_{xy}|= 2$ (ii) two counter propagating gapless edge modes. Our simple model is an example of a novel class of systems that can stabilize SPT phases protected by a continuous symmetry on lattices and opens up new possibilities for the experimental realization of these exotic phases., Comment: 7 pages, 6 figures

The non-equilibrium dynamics beyond linear response of Weyl semimetals is studied after a sudden switching on of a DC electric field. The resulting current is a nonmonotonic function of time, with an initial quick increase of polarization current followed by a power-law decay. Particle-hole creation \`a la Schwinger dominates for long times when the conduction current takes over the leading role, with the total current increasing again. The conductivity estimated from a dynamical calculation within a Drude picture agrees with the one obtained from Kubo's formula. The full distribution function of electron-hole pairs changes from Poissonian for short perturbations to a Gaussian in the long perturbation (Landau-Zener) regime. The vacuum persistence probability of high energy physics manifests itself in a finite probability of no pair creation and no induced current at all times., Comment: 7 pages, 4 figures

We study a disordered classical Heisenberg magnet with uniformly antiferromagnetic interactions which are frustrated on account of their long-range Coulomb form, {\em i.e.} $J(r)\sim -A\ln r$ in $d=2$ and $J(r)\sim A/r$ in $d=3$. This arises naturally as the $T\rightarrow 0$ limit of the emergent interactions between vacancy-induced degrees of freedom in a class of diluted Coulomb spin liquids (including the classical Heisenberg antiferromagnets on checkerboard, SCGO and pyrochlore lattices) and presents a novel variant of a disordered long-range spin Hamiltonian. Using detailed analytical and numerical studies we establish that this model exhibits a very broad paramagnetic regime that extends to very large values of $A$ in both $d=2$ and $d=3$. In $d=2$, using the lattice-Green function based finite-size regularization of the Coulomb potential (which corresponds naturally to the underlying low-temperature limit of the emergent interactions between orphan-spins), we only find evidence that freezing into a glassy state occurs in the limit of strong coupling, $A=\infty$, while no such transition seems to exist at all in $d=3$. We also demonstrate the presence and importance of screening for such a magnet. We analyse the spectrum of the Euclidean random matrices describing a Gaussian version of this problem, and identify a corresponding quantum mechanical scattering problem., Comment: two-column PRB format; 17 pages; 24 .eps figures

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 wave-vector 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, {\alpha}-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 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 {\alpha}-RuCl$_3$ as the prime candidate for experimental realization of fractionalized Kitaev physics., Comment: 15 pages, 5 figures

Ever since Heisenberg's proposal of a quantum-mechanical origin of ferromagnetism in 1928, the spin model named after him has been central to advances in magnetism, featuring in proposals of novel many-body states such as antiferromagnets, emergent gauge fields in their confined (valence bond crystal) and deconfined (resonating valence bond spin liquids) versions. Between them, these cover much of our understanding of modern magnetism specifically and topological states of matter in general. Many exciting phenomena predicted theoretically still await experimental realisation, and cold atomic systems hold the promise of acting as analogue 'quantum simulators' of the relevant theoretical models, for which ingenious and intricate set-ups have been proposed. Here, we identify a new class of particularly simple quantum simulators exhibiting many such phenomena but obviating the need for fine-tuning and for amplifying perturbatively weak superexchange or longer-range interactions. Instead they require only moderate on-site interactions on top of uncorrelated, one-body hopping--ingredients already available with present experimental technology. Between them, they realise some of the most interesting phenomena, such as emergent synthetic gauge fields, resonating valence bond phases, and even the celebrated yet enigmatic spin liquid phase of the kagome lattice., Comment: 5 pages, 4 figures

We provide a fully analytical microscopic theory for the proton correlations in water ice $I_h$. We compute the full diffuse elastic neutron scattering structure factor, which we find to be in excellent quantitative agreement with Monte Carlo simulations. It is also in remarkable qualitative agreement with experiment, in the absence of any fitting parameters. Our theory thus provides a tractable analytical starting point to account for more delicate features of the proton correlations in water ice. In addition, it directly determines an effective field theory of water ice as a topological phase., Comment: 5 pages, 3 figures

We combine two aspects of magnetic frustration, multiferroicity and emergent quasi-particles in spin liquids, by studying magneto-electric monopoles. Spin ice offers to couple these emergent topological defects to external fields, and to each other, in unusual ways, making possible to lift the degeneracy underpinning the spin liquid and to potentially stabilize novel forms of charge crystals, opening the path to a "magnetic crystallography". In developing the general phase diagram including nearest-neighbour coupling, Zeeman energy, electric and magnetic dipolar interactions, we uncover the emergence of a bi-layered crystal of singly-charged monopoles, whose stability, remarkably, is strengthened by an external [110] magnetic field. Our theory is able to account for the ordering process of Tb2Ti2O7 in large field for reasonably small electric energy scales., Comment: 10 pages, 10 figures

In this review we consider the performance of the quantum adiabatic algorithm for the solution of decision problems. We divide the possible failure mechanisms into two sets: small gaps due to quantum phase transitions and small gaps due to avoided crossings inside a phase. We argue that the thermodynamic order of the phase transitions is not predictive of the scaling of the gap with the system size. On the contrary, we also argue that, if the phase surrounding the problem Hamiltonian is a Many-Body Localized (MBL) phase, the gaps are going to be typically exponentially small and that this follows naturally from the existence of local integrals of motion in the MBL phase., Comment: 16 pages, 1 figure

We report ultrasound studies of spin-lattice and single-ion effects in the spin-ice materials Dy$_2$Ti$_2$O$_7$ (DTO) and Ho$_2$Ti$_2$O$_7$ (HTO) across a broad field range up to 60 T, covering phase transformations, interactions with low-energy magnetic excitations, as well as single-ion effects. In particular, a sharp dip observed in the sound attenuation in DTO at the gas-liquid transition of the magnetic monopoles is explained based on an approach involving negative relaxation processes. Furthermore, quasi-periodic peaks in the acoustic properties of DTO due to non-equilibrium processes are found to be strongly affected by {\em macroscopic} thermal-coupling conditions: the thermal runaway observed in previous studies in DTO can be suppressed altogether by immersing the sample in liquid helium. Crystal-electric-field effects having higher energy scale lead to a renormalization of the sound velocity and sound attenuation at very high magnetic fields. We analyze our observations using an approach based on an analysis of exchange-striction couplings and single-ion effects.

We show that, quite generically, a [111] slab of spin-orbit coupled pyrochlore lattice exhibits surface states whose constant energy curves take the shape of Fermi arcs, localized to different surfaces depending on their quasimomentum. Remarkably, these persist independently of the existence of Weyl points in the bulk. Considering interacting electrons in slabs of finite thickness, we find a plethora of known fractional Chern insulating phases, to which we add the discovery of a new higher Chern number state which is likely a generalization of the Moore-Read fermionic fractional quantum Hall state. By contrast, in the three-dimensional limit, we argue for the absence of gapped states of the flat surface band due to a topologically protected coupling of the surface to gapless states in the bulk. We comment on generalizations as well as experimental perspectives in thin slabs of pyrochlore iridates., Comment: Published. 6+4 pages