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Spin liquid crystals are magnetic analogs of liquid crystals, possessing properties of both liquids and solids, a typical example of which are spin nematics. Spin nematics share many features with spin liquids, and the interplay between them is a promising, but little explored, route to uncovering new phases of matter. Here, we address this question in the context of a spin-$1$ magnet on the honeycomb lattice, by considering a model with both biquadratic interactions, favouring spin-nematic states, and Kitaev-like interactions, supporting spin liquids. Accompanying these, where dipole and quadrupole moments compete, we find a plethora of exotic phases, including multiple-$q$ states with nonzero scalar spin chirality; a quasi-one-dimensional coplanar phase; a twisted conical phase; and a noncoplanar order state which gives way to a chiral spin liquid at finite temperature. The implication of these results for experiment is discussed., 11 pages, 9 figures

Quantum optimization algorithms offer a promising route to finding the ground states of target Hamiltonians on near-term quantum devices. None the less, it remains necessary to limit the evolution time and circuit depth as much as possible, since otherwise decoherence will degrade the computation. And even where this is done, there always exists a non-negligible error in estimates of the ground state energy. Here we present a scalable extrapolation approach to mitigating this error, which significantly improves estimates obtained using three of the most popular optimization algorithms: quantum annealing (QA), the variational quantum eigensolver (VQE), and quantum imaginary time evolution (QITE), at fixed evolution time or circuit depth. The approach is based on extrapolating the annealing time to infinity, or the variance of estimates to zero. The method is reasonably robust against noise, and for Hamiltonians which only involve few-body interactions, the additional computational overhead is an increase in the number of measurements by a constant factor. Analytic derivations are provided for the quadratic convergence of estimates of energy as a function of time in QA, and the linear convergence of estimates as a function of variance in all three algorithms. We have verified the validity of these approaches through both numerical simulation and experiments on an IBM quantum computer. This work suggests a promising new way to enhance near-term quantum computing through classical post-processing., 16 pages, 9 figures

Ca$_{10}$Cr$_7$O$_{28}$ is a novel spin-$1/2$ magnet exhibiting spin liquid behaviour which sets it apart from any previously studied model or material. However, understanding Ca$_{10}$Cr$_7$O$_{28}$ presents a significant challenge, because the low symmetry of the crystal structure leads to very complex interactions, with up to seven inequivalent coupling parameters in the unit cell. Here we explore the origin of the spin-liquid behaviour in Ca$_{10}$Cr$_7$O$_{28}$, starting from the simplest microscopic model consistent with experiment - a Heisenberg model on a single bilayer of the breathing-kagome (BBK) lattice. We use a combination of classical Monte Carlo (MC) simulation and (semi-)classical Molecular Dynamics (MD) simulation to explore the thermodynamic and dynamic properties of this model, and compare these with experimental results for Ca$_{10}$Cr$_7$O$_{28}$. We uncover qualitatively different behaviours on different timescales, and argue that the ground state of Ca$_{10}$Cr$_7$O$_{28}$ is born out of a slowly-fluctuating "spiral spin liquid", while faster fluctuations echo the U(1) spin liquid found in the kagome antiferromagnet. We also identify key differences between longitudinal and transverse spin excitations in applied magnetic field, and argue that these are a distinguishing feature of the spin liquid in the BBK model.

One of the strongest reasons for studying “quantum spin–ice” materials is the possibility that quantum tunnelling between different ice states could convert the classical magnetostatics of spin ice into a lattice analogue of quantum electrodynamics, with both magnetic and electric charges, and emergent “photon” excitations. In this Chapter we review what Quantum Monte Carlo simulations have taught us about this exotic quantum spin liquid state, and how this might help us to understand real materials.

The discovery by Kane and Mele of a model of spinful electrons characterized by a $\mathcal{Z}_2$ topological invariant had a lasting effect on the study of electronic band structures. Given this, it is natural to ask whether similar topology can be found in the band-like excitations of magnetic insulators, and recently models supporting $\mathcal{Z}_2$ topological invariants have been proposed for both magnon [Kondo et al. Phys. Rev. B 99, 041110(R) (2019)] and triplet [D. G. Joshi and A. P. Schnyder, Phys. Rev. B 100, 020407 (2019)] excitations. In both cases, magnetic excitations form time--reversal (TR) partners, which mimic the Kramers pairs of electrons in the Kane-Mele model but do not enjoy the same type of symmetry protection. In this paper, we revisit this problem in the context of the triplet excitations of a spin model on the bilayer kagome lattice. Here the triplet excitations provide a faithful analog of the Kane-Mele model as long as the Hamiltonian preserves the TR$\times$U(1) symmetry. We find that exchange anisotropies, allowed by the point group and typical in realistic models, break the required TR$\times$U(1) symmetry and instantly destroy the $\mathcal{Z}_2$ band topology. We further consider the effects of TR breaking by an applied magnetic field. In this case, the lifting of spin-degeneracy leads to a triplet Chern insulator, which is stable against the breaking of TR$\times$U(1) symmetry. Kagome bands realize both a quadratic and a linear band touching, and we provide a thorough characterization of the Berry curvature associated with both cases. We also calculate the triplet-mediated spin Nernst and thermal Hall signals which could be measured in experiments. These results suggest that the $\mathcal{Z}_2$ topology of band-like excitations in magnets may be intrinsically fragile compared to their electronic counterparts., Comment: 19 pages, 16 figures

20 pages, 15 figures, 3 tables; International audience; Machine-learning techniques have proved successful in identifying ordered phases of matter. However, it remains an open question how far they can contribute to the understanding of phases without broken symmetry, such as spin liquids. Here we demonstrate how a machine-learning approach can automatically learn the intricate phase diagram of a classical frustrated spin model. The method we employ is a support vector machine equipped with a tensorial kernel and a spectral graph analysis which admits its applicability in an effectively unsupervised context. Thanks to the interpretability of the machine we are able to infer, in closed form, both order parameter tensors of phases with broken symmetry, and the local constraints which signal an emergent gauge structure, and so characterize classical spin liquids. The method is applied to the classical XXZ model on the pyrochlore lattice where it distinguishes, among others, between a hidden biaxial spin-nematic phase and several different classical spin liquids. The results are in full agreement with a previous analysis by Taillefumier et al. [Phys. Rev. X 7, 041057 (2017)], but go further by providing a systematic hierarchy between disordered regimes, and establishing the physical relevance of the susceptibilities associated with the local constraints. Our work paves the way for the search of new orders and spin liquids in generic frustrated magnets.

We report neutron-scattering and ac magnetic susceptibility measurements of the two-dimensional spin-1/2 frustrated magnet $\mathrm{BaCdVO}{({\mathrm{PO}}_{4})}_{2}$. At temperatures well below ${T}_{\mathsf{N}}\ensuremath{\approx}1\phantom{\rule{4.pt}{0ex}}\text{K}$, we show that only 34% of the spin moment orders in an up-up-down-down stripe structure. Dominant magnetic diffuse scattering and comparison to published $\mathrm{muon}\ensuremath{-}\mathrm{spin}\ensuremath{-}\mathrm{rotation}$ measurements indicates that the remaining 66% is fluctuating. This demonstrates the presence of strong frustration, associated with competing ferromagnetic and antiferromagnetic interactions, and points to a subtle ordering mechanism driven by magnon interactions. On applying magnetic field, we find that at $T=0.1$ K the magnetic order vanishes at 3.8 T, whereas magnetic saturation is reached only above 4.5 T. We argue that the putative high-field phase is a realization of the long-sought bond-spin-nematic state.

Higher-rank generalisations of electrodynamics have recently attracted considerable attention because of their ability to host "fracton" excitations, with connections to both quantum stabilizer codes and holography. However, the search for higher-rank gauge theories in experiment has been greatly hindered by the lack of materially-relevant microscopic models. Here we show how a spin liquid described by rank-2 $U(1)$ gauge theory can arise in a magnet on the breathing pyrochlore lattice. We identify Yb-based breathing pyrochlores as candidate systems, and make explicit predictions for how the rank-2 $U(1)$ spin liquid would manifest itself in experiment., Comment: 5 pages, 4 figures, with supplemental material. To appear on Phys. Rev. Lett

We report on negative thermal expansion (NTE) in the high-field, half-magnetization plateau phase of the frustrated magnetic insulator CdCr2O4. Using dilatometry, we precisely map the phase diagram at fields of up to 30T, and identify a strong NTE associated with the collinear half-magnetization plateau for B > 27T. The resulting phase diagram is compared with a microscopic theory for spin-lattice coupling, and the origin of the NTE is identified as a large negative change in magnetization with temperature, coming from a nearly-localised band of spin excitations in the plateau phase. These results provide useful guidelines for the discovery of new NTE materials., 6 pages, 2 figures

"Pinch points," singular features observed in (quasi-)elastic neutron scattering, are a widely discussed hallmark of spin liquids with an emergent gauge symmetry. Much less attention has been paid to "half moons," distinctive crescent patterns at finite energy, which have been observed in experiments on a number of pyrochlore magnets, and in a wide range of model calculations. Here we unify these two phenomena within a single framework, paying particular attention to the case of ordered, or field-saturated states, where pinch points and half moons can be found in bands of excitations above a gap. We find that half moons are nothing other than pinch points inscribed on a dispersing band. Molecular dynamics simulations of the kagome lattice antiferromagnet are used to explore how these bands evolve into the ground state and excitations of a classical spin liquid. We explicitly demonstrate that this theory can reproduce the pinch points and half moons observed in Nd$_2$Zr$_2$O$_7$., 6 pages, 4 figures. Supplementary material: 10 pages, 3 figures

Quantum spin ice materials, pyrochlore magnets with competing Ising and transverse exchange interactions, have been widely discussed as candidates for a quantum spin-liquid ground state. Here, motivated by quantum chemical calculations for Pr pyrochlores, we present the results of a study for frustrated transverse exchange. Using a combination of variational calculations, exact diagonalisation, numerical linked-cluster and series expansions, we find that the previously-studied U(1) quantum spin liquid, in its pi-flux phase, transforms into a nematic quantum spin liquid at a high-symmetry, SU(2) point., 5 pages in main text, 10 pages supplemental material

Graphene quantum dots (GQD's) have optical properties which are very different from those of an extended graphene sheet. In this Article we explore how the size, shape and edge--structure of a GQD affect its optical conductivity. Using representation theory, we derive optical selection rules for regular-shaped dots, starting from the symmetry properties of the current operator. We find that, where the x- and y-components of the current operator transform with the same irreducible representation (irrep) of the point group - for example in triangular or hexagonal GQD's - the optical conductivity is independent of the polarisation of the light. On the other hand, where these components transform with different irreps - for example in rectangular GQD's - the optical conductivity depends on the polarisation of light. We find that GQD's with non-commuting point-group operations - for example dots of rectangular shape - can be distinguished from GQD's with commuting point-group operations - for example dots of triangular or hexagonal shape - by using polarized light. We carry out explicit calculations of the optical conductivity of GQD's described by a simple tight--binding model and, for dots of intermediate size, \textcolor{blue}{($10 \lesssim L \lesssim 50\ \text{nm}$)} find an absorption peak in the low--frequency range of the spectrum which allows us to distinguish between dots with zigzag and armchair edges. We also clarify the one-dimensional nature of states at the van Hove singularity in graphene, providing a possible explanation for very high exciton-binding energies. Finally we discuss the role of atomic vacancies and shape asymmetry., 24 pages, 15 figures

The family of magnetic rare-earth pyrochlore oxides R2M2O7 plays host to a diverse array of exotic phenomena, driven by the interplay between geometrical frustration and spin-orbit interaction, which leads to anisotropy in both magnetic moments and their interactions. In this article we establish a general, symmetry-based theory of pyrochlore magnets with anisotropic exchange interactions. Starting from a very general model of nearest-neighbor exchange between Kramers ions, we find four distinct classical ordered states, all with q=0, competing with a variety of spin liquids and unconventional forms of magnetic order. The finite-temperature phase diagram of this model is determined by Monte Carlo simulation, supported by classical spin-wave calculations. We pay particular attention to the region of parameter space relevant to the widely studied materials Er2Ti2O7, Yb2Ti2O7, and Er2Sn2O7. We find that many of the most interesting properties of these materials can be traced back to the “accidental” degeneracies where phases with different symmetries meet. These include the ordered ground-state selection by fluctuations in Er2Ti2O7, the dimensional reduction observed in Yb2Ti2O7, and the lack of reported magnetic order in Er2Sn2O7. We also discuss the application of this theory to other pyrochlore oxides.

The influence of electrostatic interactions on the ordering of sodium ions in Na$_x$CoO$_2$ is studied theoretically through Monte-Carlo simulations. For large $x$ small di- or tri-vacancy clusters are stable with respect to isolated Na vacancies. At commensurate fillings these small clusters order in triangular superstructures. These results agree with recent electron diffraction data at $x=1/2$ and 3/4. We have performed neutron La\"ue diffraction experiments at higher $x$, which confirm the predictions of this simple model. The consequences on the properties of the electronic charges in the Co layers are discussed., Comment: Talk at LT24 International Conference, Orlando, FLO, USA. August 2005. Accepted for publication in LT24 Conference Proceedings (AIP. Proc.). 2 pages, 4 figures

There is now strong theoretical evidence that a wide range of frustrated magnets should support quantum spin-nematic order in an applied magnetic field. Nonetheless, the fact that spin-nematic order does not break time-reversal symmetry makes it very difficult to detect in experiment. In this article, we continue the theme begun in Phys. Rev. B 88, 184430 (2013), of exploring how spin-nematic order reveals itself in the spectrum of spin excitations. Building on an earlier analysis of inelastic neutron scattering [Phys. Rev. B 91, 174402 (2015)], we show how the NMR 1/T-1 relaxation rate could be used to identify a spin-nematic state in an applied magnetic field. We emphasize the characteristic universal features of 1/T-1 using a symmetry-based description of the spin-nematic order parameter and its fluctuations. Turning to the specific case of spin-1/2 frustrated ferromagnets, we show that the signal from competing spin-wave excitations can be suppressed through a judicious choice of nuclear site and field direction. As a worked example, we show how P-31 NMR in the square lattice frustrated ferromagnet BaCdVO(PO4)(2) is sensitive to spin-nematic order.

If magnetic frustration is most commonly known for undermining long-range order, as famously illustrated by spin liquids, the ability of matter to develop new collective mechanisms in order to fight frustration is perhaps no less fascinating, providing an avenue for the exploration and discovery of unconventional behaviors. Here, we study a realistic minimal model where a number of such mechanisms converge, which, incidentally, pertain to the perplexing quantum spin ice candidate Yb(2)Ti(2)O(7). Specifically, we explain how thermal and quantum fluctuations, optimized by order-by-disorder selection, conspire to expand the stability region of a degenerate continuous U(1) manifold against the classical splayed ferromagnetic ground state that is displayed by the sister compound Yb(2)Ti(2)O(7). The resulting competition gives rise to multiple phase transitions, in striking similitude with recent experiments on Yb(2)Ti(2)O(7) [Lhotel et al., Phys. Rev. B 89, 224419 (2014)]. By combining a gamut of numerical techniques, we obtain compelling evidence that such multiphase competition is a natural engine for the substantial sample-to-sample variability observed in Yb(2)Ti(2)O(7) and is the missing key to ultimately understand the intrinsic properties of this material. As a corollary, our work offers a pertinent illustration of the influence of chemical pressure in rare-earth pyrochlores.

Cold atoms bring new opportunities to study quantum magnetism, and in particular, to simulate quantum magnets with symmetry greater than $SU(2)$. Here we explore the topological excitations which arise in a model of cold atoms on the triangular lattice with $SU(3)$ symmetry. Using a combination of homotopy analysis and analytic field-theory we identify a new family of solitonic wave functions characterised by integer charge ${\bf Q} = (Q_A, Q_B, Q_C)$, with $Q_A + Q_B + Q_C = 0$. We use a numerical approach, based on a variational wave function, to explore the stability of these solitons on a finite lattice. We find that, while solitons with charge ${\bf Q} = (Q, -Q, 0)$ are stable, wave functions with more general charge spontaneously decay into pairs of solitons with emergent interactions. This result suggests that it could be possible to realise a new class of interacting soliton, with no classical analogue, using cold atoms. It also suggests the possibility of a new form of quantum spin liquid, with gauge--group U(1)$\times$U(1)., 8 pages, 5 figures

Magnetic pyrochlore oxides, including the spin ice materials, have proved to be a rich field for the study of geometrical frustration in 3 dimensions. Recently, a new family of magnetic oxides has been synthesised in which the half of the tetrahedra in the pyrochlore lattice are inflated relative to the other half, making an alternating array of small and large tetrahedra. These "breathing pyrochlore" materials such as LiGaCr4O8, LiInCr4O8 and Ba3Yb2Zn5O11 provide new opportunities in the study of frustrated magnetism. Here we provide an analytic theory for the ground state phase diagram and spin correlations for the minimal model of magnetism in breathing pyrochlores: a classical nearest neighbour Heisenberg model with different exchange coefficients for the two species of tetrahedra. We find that the phase diagram comprises a Coulombic spin liquid phase, a conventional ferromagnetic phase and an unusual antiferromagnetic phase with lines of soft modes in reciprocal space, stabilised by an order-by-disorder mechanism. We obtain a theory of the spin correlations in this model using the Self Consistent Gaussian Approximation (SCGA) which enables us to discuss the development of correlations in breathing pyrochlores as a function of temperature, and we quantitatively characterise the thermal crossover from the limit of isolated tetrahedra to the strongly correlated limit of the problem. We compare the results of our analysis with the results of recent neutron scattering experiments on LiInCr4O8., 12 pages, 10 figures

If magnetic frustration is most commonly known for undermining long-range order, as famously illustrated by spin liquids, the ability of matter to develop new collective mechanisms in order to fight frustration is perhaps no less fascinating, providing an avenue for the exploration and discovery of unconventional behaviors. Here, we study a realistic minimal model where a number of such mechanisms converge, which, incidentally, pertain to the perplexing quantum spin ice candidate Yb(2)Ti(2)O(7). Specifically, we explain how thermal and quantum fluctuations, optimized by order-by-disorder selection, conspire to expand the stability region of a degenerate continuous U(1) manifold against the classical splayed ferromagnetic ground state that is displayed by the sister compound Yb(2)Ti(2)O(7). The resulting competition gives rise to multiple phase transitions, in striking similitude with recent experiments on Yb(2)Ti(2)O(7) [Lhotel et al., Phys. Rev. B 89, 224419 (2014)]. By combining a gamut of numerical techniques, we obtain compelling evidence that such multiphase competition is a natural engine for the substantial sample-to-sample variability observed in Yb(2)Ti(2)O(7) and is the missing key to ultimately understand the intrinsic properties of this material. As a corollary, our work offers a pertinent illustration of the influence of chemical pressure in rare-earth pyrochlores.

We develop a theory of spin excitations in a field-induced spin-nematic state, and use it to show how a spin-nematic order can be indentified using inelastic neutron scattering. We concentrate on two-dimensional frustrated ferromagnets, for which a two-sublattice, bond-centered spin-nematic state is predicted to exist over a wide range of parameters. First, to clarify the nature of spin-excitations, we introduce a soluble spin-1 model, and use this to derive a continuum field theory, applicable to any two-sublattice spin-nematic state. We then parameterize this field theory, using diagrammatic calculations for a realistic microscopic model of a spin-1/2 frustrated ferromagnet, and show how it can be used to make predictions for inelastic neutron scattering. As an example, we show quantitative predictions for inelastic scattering of neutrons from BaCdVO(PO4)(2), a promising candidate to realize a spin-nematic state at an achievable h similar to 4 T. We show that in this material it is realistic to expect a ghostly Goldstone mode, signalling spin-nematic order, to be visible in experiment.

It has been known since the pioneering work of Bernal, Fowler and Pauling that common, hexagonal (Ih) water ice is the archetype of a frustrated material : a proton-bonded network in which protons satisfy strong local constraints - the "ice rules" - but do not order. While this proton disorder is well established, there is now a growing body of evidence that quantum effects may also have a role to play in the physics of ice at low temperatures. In this Article we use a combination of numerical and analytic techniques to explore the nature of proton correlations in both classical and quantum models of ice Ih. In the case of classical ice Ih, we find that the ice rules have two, distinct, consequences for scattering experiments - singular "pinch points", reflecting a zero-divergence condition on the uniform polarization of the crystal, and broad, asymmetric features, coming from its staggered polarisation. In the case of the quantum model, we find that the collective quantum tunnelling of groups of protons can convert states obeying the ice rules into a quantum liquid, whose excitations are birefringent, emergent photons. We make explicit predictions for scattering experiments on both classical and quantum ice Ih, and show how the quantum theory can explain the "wings" of incoherent inelastic scattering observed in recent neutron scattering experiments [Bove et al., Phys. Rev. Lett. 103, 165901 (2009)]. These results raise the intriguing possibility that the protons in ice Ih could form a quantum liquid at low temperatures, in which protons are not merely disordered, but continually fluctuate between different configurations obeying the ice rules., 33 pages (21 in main text), 13 figures (9 in main text), expanded discussion of experiment with new subsection on thermodynamics

A large part of the interest in magnets with frustrated antiferromagnetic interactions comes from the many new phases found in applied magnetic field. In this Article, we explore some of the new phases which arise in a model with frustrated ferromagnetic interactions, the $J_1-J_2-J_3$ Heisenberg model on a square lattice. Using a combination of classical Monte-Carlo simulation and spin-wave theory, we uncover behaviour reminiscent of some widely-studied frustrated antiferromagnets, but with a number of new twists. We first demonstrate that, for a suitable choice of parameters, the phase diagram as a function of magnetic field and temperature is nearly identical to that of the Heisenberg antiferromagnet on a triangular lattice, including the celebrated 1/3-magnetisation plateau. We then examine how this phase diagram changes when the model is tuned to a point where the classical ground--state is highly degenerate. In this case, two new phases emerge; a classical, finite-temperature spin-liquid, characterised by a "ring" in the spin structure--factor $\mathcal{S}({\mathbf q})$; and a vortex crystal, a multiple-Q state with finite magnetisation, which can be viewed as an ordered lattice of magnetic vortices. All of these new phases persist for a wide range of magnetic field. We discuss the relationship between these results and published studies of frustrated antiferromagnets, together with some of the materials where these new phases might be observed in experiment., Comment: 23 pages, 17 figures, as published

We discuss the possibility of finding n-type nematic order in the vicinity of a FM phase in the multiple--spin exchange model on the triangular lattice. We study this problem both from S=\infty (classical) and S=1/2 (quantum) limits., 5 pages, 3 figures, Proceedings of QSS04

Crystal and magnetic structures of bilayer (n = 2) Ruddlesden-Popper phase La1-2x Sr1+2x Mn2O7 have been reviewed and their relationship with the colossal magnetoresistive behavior discussed. Experimental results of inelastic and quasielastic neutron scattering on the 40% hole-doped (x = 0.4) bilayer man-ganite La1.2Sr1.8Mn2O7 have been described. A fully quantum theory of the spin dynamics of ferromagnetic manganites is developed, starting from the minimal double exchange model. This is compared with experimental results for a ferromagnetic bilayer system. A mean-field type theory of doping dependence of the exchange interactions in bilayer manganites has also been developed and compared is compared with the experimental results.

A pyrochlore lattice is considered where the average electron number of electrons per site is half--integer, concentrating on the case of exactly half an electron per site. Strong on-site repulsions are assumed, so that all sites are either empty or singly occupied. Where there are in addition strong nearest--neighbour repulsions, a tetrahedron rule comes into effect, as previously suggested for magnetite. We show that in this case, there exist excitations with fractional charge (+/-) e/2. These are intimately connected with the high degeneracy of the ground state in the absence of kinetic energy terms. When an additional electron is inserted into the system, it decays into two point like excitations with charge -e/2, connected by a Heisenberg spin chain which carries the electron's spin., Comment: 10 pages, 4 eps figures. To appear in Decemeber issue of Annalen der Physik

We construct a theory of spin wave excitations in the bilayer manganite La(1.2)Sr(1.8)Mn2O7 based on the simplest possible double-exchange model, but including leading quantum corrections to the spin wave dispersion and damping. Comparison is made with recent inelastic neutron scattering experiments. We find that quantum effects account for some part of the measured damping of spin waves, but cannot by themselves explain the observed softening of spin waves at the zone boundary. Furthermore a doping dependence of the total spin wave dispersion and the optical spin wave gap is predicted.

Frustrated magnets can exhibit many novel forms of order when exposed to high magnetic fields, however, much less is known about materials where frustration occurs in the presence of itinerant electrons. Here we report thermodynamic and transport measurements on micron-sized single crystals of the triangular-lattice metallic antiferromagnet 2H-AgNiO2, in magnetic fields of up to 90 T and temperatures down to 0.35 K. We observe a cascade of magnetic phase transitions at 13.5 20, 28 and 39T in fields applied along the easy axis, and we combine magnetic torque, specific heat and transport data to construct the field-temperature phase diagram. The results are discussed in the context of a frustrated easy-axis Heisenberg model for the localized moments where intermediate applied magnetic fields are predicted to stabilize a magnetic supersolid phase. Deviations in the measured phase diagram from this model predictions are attributed to the role played by the itinerant electrons., Comment: possible experimental signature of a magnetic supersolid phase

Recent experiments on the spin-ice material Dy2Ti2O7 suggest that the Pauling "ice entropy", characteristic of its classical Coulombic spin-liquid state, may be lost at low temperatures [D. Pomaranski et al., Nature Phys. 9, 353 (2013)]. However, despite nearly two decades of intensive study, the nature of the equilibrium ground state of spin ice remains uncertain. Here we explore how long-range dipolar interactions D, short-range exchange interactions, and quantum fluctuations combine to determine the ground state of dipolar spin ice. We identify a new organisational principle, namely that ordered ground states are selected from a set of "chain states" in which dipolar interactions are exponentially screened. Using both quantum and classical Monte Carlo simulation, we establish phase diagrams as a function of quantum tunneling g, and temperature T, and find that only a very small g_c << D is needed to stabilize a quantum spin-liquid ground state. We discuss the implications of these results for Dy2Ti2O7., 24 pages

Core-hole (x-ray) photoemission (XPS) provides a powerful indirect probe of the low-energy charge excitations of a many-electron system. We have previously argued that XPS can be used to study the way in which a (pseudo)gap opens for charge excitations across, for example, a metal-superconductor transition, independently of any change in the spin excitation spectrum, and so provide information about spin-charge separation. Here we consider how the loss of low-energy excitations modifies XPS spectra in the context of several simple models, considering particularly the case of gap opening for both s- and d-wave superconductors, and find that XPS, like the nuclear magnetic resonance technique, is in principle sensitive to nodes in the superconducting gap function.

Kondo lattice models are widely used to describe systems where local magnetic moments couple to itinerant electrons. We construct a novel large S expansion scheme for an ordered Kondo lattice, starting from the eigenstates of the Kondo coupling on a single site, and paying particular attention to the special case of two sites sharing a single electron, which we solve exactly. The expansion scheme which we introduce is shown to reproduce all features of this exact solution, to O(1/S2), and to offer a better physical starting point than previous approaches for calculating the properties of systems on a lattice in the `double exchange' limit of strong Hund's rule coupling.

The possibility that strongly correlated many-electron systems may exhibit spin-charge separation has generated great excitement, particularly in the light of recent experiments on low-dimensional conductors and high-temperature superconductors. However, finding experimental support for this hypothesis has been made difficult by the fact that most commonly used probes couple simultaneously to spin and charge excitations. We argue that core-hole photoemission (XPS)/nuclear magnetic resonance (NMR) couple independently and in exactly comparable ways to the local charge/spin susceptibilities of the system being measured. The explicit comparison of XPS and NMR data, particularly for systems which exhibit a pseudogap, may therefore yield fresh evidence for the existence (or non-existence) of spin-charge separation. Application of these ideas to the normal state of high-temperature superconductors is discussed, and the application is further illustrated in some detail for quasi-one-dimensional systems with charge-density waves.

The room temperature ``metallic'' properties of the quasi-one-dimensional charge density wave system (TaSe4)2I differ markedly from those expected of either a Fermi or a Luttinger Liquid. We discuss evidence for the simplest possible explanation of the observed behavior of (TaSe4)2I in its conducting phase - namely the existence of large quasi-static fluctuations of structural order, which however remain of finite extent above the charge density wave transition temperature. These fluctuations produce a pseudogap in the density of states. We compute the temperature dependence of the optical and DC conductivities of (TaSe4)2I in its conducting phase, the nature of its core hole spectra, and the NMR relaxation rate. Predictions for these quantities are made on the basis of a Lee, Rice and Anderson model. This model represents the simplest theory of a pseudogap, and gives satisfactory agreement with experiment in the cases where comparisons can be made. In contrast, the predictions of a strongly correlated (Luttinger Liquid) model appear to to contradict the data. The chief remaining discrepancy is that the gap appearing in transport quantities is less than that observed in photoemission. We discuss some possibilities for resolving this issue.

We have measured the diffuse scattering of polarized neutrons in the paramagnetic phase of La2CuO4 using the IN20 spectrometer at the Institut Laue-Langevin. The dynamical response is shown to be in full agreement with the predictions of the quantum nonlinear sigma model. The staggered susceptibilty has been placed on an absolute scale to facilitate the comparison of our data with theoretical models. New calculations of the high-temperature series expansion of the spin correlations in the paramagnetic phase provide compelling, quantitative evidence for the existence of four-particle ring exchange.

We discuss the thermodynamics of the two-dimensional frustrated J 1 – J 2 Heisenberg model on a square lattice in a magnetic field. In particular we address the behaviour of the heat capacity and the saturation field of the magnetisation as a function of the frustration parameter of the model. We relate our numerical findings to the compounds which were investigated experimentally and propose a new way to unambiguously determine the ground state of a specific J 1 – J 2 compound.

The long-range three-dimensional ordering of Na + ions was studied in a sample of composition Na 0.75 CoO 2 using single-crystal neutron diffraction. Large-scale numerical simulations reveal the ordering principle for this system, the formation of multi-vacancy charged droplets then order long range, and the structure factors from these defect clusters are in good agreement with the observed neutron diffraction intensities. The electrostatic potential is found to be the dominant factor in determining the sodium ordering and its associated distortion field. The superstructures induce a periodic potential in the CoO 2 , giving potential wells that are larger than the single-particle hopping frequency and so able to localize holes. The results readily explain many of the observed electrical and magnetic properties, including the three dimensionality of the magnetic excitations.

We present a detailed numerical study of the orthogonality catastrophe exponent for a one-dimensional lattice model of spinless fermions with nearest neighbor interaction using the density matrix remormalization group algorithm. Keeping up to 1200 states per block we achieve a very great accuracy for the overlap which is needed to extract the orthogonality exponent reliably. We discuss the behavior of the exponent for three different kinds of a localized impurity. For comparison we also discuss the non-interacting case. In the weak impurity limit our results for the overlap confirm scaling behavior expected from perturbation theory and renormalization group calculations. In particular we find that a weak backward scattering component of the orthogonality exponent scales to zero for attractive interaction. In the strong impurity limit and for repulsive interaction we demonstrate that the orthogonality exponent cannot be extracted from the overlap for systems with up to 100 sites, due to finite size effects. This is in contradiction to an earlier interpretation given by Qin et al. based on numerical data for much smaller system sizes. Neverthless we find indirect evidence that the backward scattering contribution to the exponent scales to 1/16 based on predictions of boundary conformal field theory., 16 pages, Latex, 8 eps figures, submitted to Phys. Rev. B

The idea that a quantum magnet could act like a liquid crystal, breaking spin-rotation symmetry without breaking time-reversal symmetry, holds an abiding fascination. However, the very fact that spin nematic states do not break time-reversal symmetry renders them "invisible" to the most common probes of magnetism - they do not exhibit magnetic Bragg peaks, a static splitting of lines in NMR spectra, or oscillations in μSR. Nonetheless, as a consequence of breaking spin-rotation symmetry, spin-nematic states do possess a characteristic spectrum of dispersing excitations which could be observed in experiment. With this in mind, we develop a symmetry-based description of long-wavelength excitations in a spin-nematic state, based on an SU(3) generalization of the quantum nonlinear σ model. We use this field theory to make explicit predictions for inelastic neutron scattering, and argue that the wavelike excitations it predicts could be used to identify the symmetries broken by the otherwise unseen spin-nematic order. © 2013 American Physical Society.

The competition between different and unusual effects in quasi-one-dimensional conductors makes the direct interpretation of experimental measurements of these materials both difficult and interesting. We consider evidence for the existence of large charge-density-wave fluctuations in the conducting phase of the Peierls insulator (TaSe4)2I, by comparing the predictions of a simple Lee, Rice and Anderson theory for such a system with recent angle-resolved photoemission spectra. The agreement obtained suggests that many of the unusual features of these spectra may be explained in this way. This view of the system is contrasted with the behaviour expected of a Luttinger liquid.

The "spin ice" state found in the rare earth pyrochlore magnets Ho2Ti2O7 and Dy2Ti2O7 offers a beautiful realisation of classical magnetostatics, complete with magnetic monopole excitations. It has been suggested that in "quantum spin ice" materials, quantum-mechanical tunnelling between different ice configurations could convert the magnetostatics of spin ice into a quantum spin liquid which realises a fully dynamical, lattice-analogue of quantum electromagnetism. Here we explore how such a state might manifest itself in experiment, within the minimal microscopic model of a such a quantum spin ice. We develop a lattice field theory for this model, and use this to make explicit predictions for the dynamical structure factor which would be observed in neutron scattering experiments on a quantum spin ice. We find that "pinch points", seen in quasi-elastic scattering, which are the signal feature of a classical spin ice, fade away as a quantum ice is cooled to its zero-temperature ground state. We also make explicit predictions for the ghostly, linearly dispersing magnetic excitations which are the "photons" of this emergent electromagnetism. The predictions of this field theory are shown to be in quantitative agreement with Quantum Monte Carlo simulations at zero temperature., 26 pages, 18 figures, minor revisions