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The dynamics of superfluid 4He at and above the Landau quasiparticle regime is investigated by high precision inelastic neutron scattering measurements of the dynamic structure factor. A highly structured response is observed above the familiar phonon-maxon-roton spectrum, characterized by sharp thresholds for phonon-phonon, maxon-roton and roton-roton coupling processes. The experimental dynamic structure factor is compared to the calculation of the same physical quantity by a Dynamic Many-body theory including three-phonon processes self-consistently. The theory is found to provide a quantitative description of the dynamics of the correlated bosons for energies up to about three times that of the Landau quasiparticles., Comment: 5 pages, 3 figures

The ground-state (GS) phase diagram of the frustrated spin-$s$ $J_{1}$--$J_{2}$--$J_{3}$ Heisenberg antiferromagnet on the honeycomb lattice is studied using the coupled cluster method, for spin quantum numbers $s=1,\,\frac{3}{2},\,2\,,\frac{5}{2}$. We study the case $J_{3}=J_{2}=\kappa J_{1}$, in the range $0 \leq \kappa \leq 1$, which includes the point of maximum classical ($s \to \infty$) frustration, viz., the classical critical point at $\kappa_{{\rm cl}}=\frac{1}{2}$, separating the N\'{e}el phase for $\kappa < \kappa_{{\rm cl}}$ and the collinear striped AFM phase for $\kappa > \kappa_{{\rm cl}}$. Results are presented for the GS energy, magnetic order parameter and plaquette valence-bond crystal (PVBC) susceptibility. For all spins $s \geq \frac{3}{2}$ we find a quantum phase diagram very similar to the classical one, with a direct first-order transition between the two collinear AFM states at a value $\kappa_{c}(s)$ which is slightly greater than $\kappa_{{\rm cl}}$ [e.g., $\kappa_{c}(\frac{3}{2}) \approx 0.53(1)$] and which approaches it monotonically as $s \to \infty$. By contrast, for the case $s=1$ the transition is split into two such that the stable GS phases are ones with N\'{e}el AFM order for $\kappa < \kappa_{c_{1}} = 0.485(5)$ and with striped AFM order for $\kappa > \kappa_{c_{2}} = 0.528(5)$, just as in the case $s=\frac{1}{2}$ (for which $\kappa_{c_{1}} \approx 0.47$ and $\kappa_{c_{2}} \approx 0.60$). For both the $s=\frac{1}{2}$ and $s=1$ models the transition at $\kappa_{c_{2}}$ appears to be of first-order type, while that at $\kappa_{c_{1}}$ appears to be continuous. However, whereas in the $s=\frac{1}{2}$ case the intermediate phase appears to have PVBC order over the entire range $\kappa_{c_{1}} < \kappa < \kappa_{c_{2}}$, in the $s=1$ case PVBC ordering either exists only over a very small part of the region or, more likely, is absent everywhere.

We use the coupled cluster method implemented to high orders of approximation to investigate the frustrated spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$--$J_{3}$ antiferromagnet on the honeycomb lattice with isotropic Heisenberg interactions of strength $J_{1} > 0$ between nearest-neighbor pairs, $J_{2}>0$ between next-nearest-neighbor pairs, and $J_{3}>0$ between next-next-neareast-neighbor pairs of spins. In particular, we study both the ground-state (GS) and lowest-lying triplet excited-state properties in the case $J_{3}=J_{2} \equiv \kappa J_{1}$, in the window $0 \leq \kappa \leq 1$ of the frustration parameter, which includes the (tricritical) point of maximum classical frustration at $\kappa_{{\rm cl}} = \frac{1}{2}$. We present GS results for the spin stiffness, $\rho_{s}$, and the zero-field uniform magnetic susceptibility, $\chi$, which complement our earlier results for the GS energy per spin, $E/N$, and staggered magnetization, $M$, to yield a complete set of accurate low-energy parameters for the model. Our results all point towards a phase diagram containing two quasiclassical antiferromagnetic phases, one with N\'eel order for $\kappa < \kappa_{c_{1}}$, and the other with collinear striped order for $\kappa > \kappa_{c_{2}}$. The results for both $\chi$ and the spin gap $\Delta$ provide compelling evidence for a quantum paramagnetic phase that is gapped over a considerable portion of the intermediate region $\kappa_{c_{1}} < \kappa < \kappa_{c_{2}}$, especially close to the two quantum critical points at $\kappa_{c_{1}}$ and $\kappa_{c_{2}}$. Each of our fully independent sets of results for the low-energy parameters is consistent with the values $\kappa_{c_{1}} = 0.45 \pm 0.02$ and $\kappa_{c_{2}} = 0.60 \pm 0.02$, and with the transition at $\kappa_{c_{1}}$ being of continuous (and probably of the deconfined) type and that at $\kappa_{c_{2}}$ being of first-order type.

We outline how the coupled cluster method of microscopic quantum many-body theory can be utilized in practice to give highly accurate results for the ground-state properties of a wide variety of highly frustrated and strongly correlated spin-lattice models of interest in quantum magnetism, including their quantum phase transitions. The method itself is described, and it is shown how it may be implemented in practice to high orders in a systematically improvable hierarchy of (so-called LSUB$m$) approximations, by the use of computer-algebraic techniques. The method works from the outset in the thermodynamic limit of an infinite lattice at all levels of approximation, and it is shown both how the "raw" LSUB$m$ results are themselves generally excellent in the sense that they converge rapidly, and how they may accurately be extrapolated to the exact limit, $m \rightarrow \infty$, of the truncation index $m$, which denotes the {\it only} approximation made. All of this is illustrated via a specific application to a two-dimensional, frustrated, spin-half $J^{XXZ}_{1}$--$J^{XXZ}_{2}$ model on a honeycomb lattice with nearest-neighbor and next-nearest-neighbor interactions with exchange couplings $J_{1}>0$ and $J_{2} \equiv \kappa J_{1} > 0$, respectively, where both interactions are of the same anisotropic $XXZ$ type. We show how the method can be used to determine the entire zero-temperature ground-state phase diagram of the model in the range $0 \leq \kappa \leq 1$ of the frustration parameter and $0 \leq \Delta \leq 1$ of the spin-space anisotropy parameter. In particular, we identify a candidate quantum spin-liquid region in the phase space.

We study the zero-temperature ($T=0$) ground-state (GS) properties of a frustrated spin-half $J^{XXZ}_{1}$--$J^{XXZ}_{2}$ model on the honeycomb lattice with nearest-neighbor and next-nearest-neighbor interactions with exchange couplings $J_{1}>0$ and $J_{2} \equiv \kappa J_{1}>0$, respectively, using the coupled cluster method. Both interactions are of the anisotropic $XXZ$ type. We present the $T=0$ GS phase diagram of the model in the ranges $0 \leq \Delta \leq 1$ of the spin-space anisotropy parameter and $0 \leq \kappa \leq 1$ of the frustration parameter. A possible quantum spin-liquid region is identified.

We study the zero-temperature ground-state (GS) phase diagram of a spin-half $J_{1}$--$J_{2}$ $XY$ model on the honeycomb lattice with nearest-neighbor exchange coupling $J_{1}>0$ and frustrating next-nearest-neighbor exchange coupling $J_{2} \equiv \kappa J_{1}>0$, where both bonds are of the isotropic $XY$ type, using the coupled cluster method. Results are presented for the GS energy per spin, magnetic order parameter, and staggered dimer valence-bond crystalline (SDVBC) susceptibility, for values of the frustration parameter in the range $0 \leq \kappa \leq 1$. In this range we find phases exhibiting, respectively, N\'{e}el $xy$ planar [N(p)], N\'{e}el $z$-aligned [N($z$)], SDVBC, and N\'{e}el-II $xy$ planar [N-II(p)] orderings which break the lattice rotational symmetry. The N(p) state, which is stable for the classical version of the model in the range $0 \leq \kappa \leq \frac{1}{6}$, is found to form the GS phase out to a first quantum critical point at $\kappa_{c_{1}} = 0.216(5)$, beyond which the stable GS phase has N($z$) order over the range $\kappa_{c_{1}} < \kappa < \kappa_{c_{2}}=0.355(5)$. For values $\kappa > \kappa_{c_{2}}$ we find a strong competition to form the GS phase between states with N-II(p) and SDVBC forms of order. Our best estimate, however, is that the stable GS phase over the range $\kappa_{c_{2}} < \kappa < \kappa_{c_{3}} \approx 0.52(3)$ is a mixed state with both SDVBC and N-II(p) forms of order; and for values $\kappa > \kappa_{c_{3}}$ is the N-II(p) state, which is stable at the classical level only at the highly degenerate point $\kappa=\frac{1}{2}$. Over the range $0 \leq \kappa \leq 1$ we find no evidence for any of the spiral phases that are present classically for all values $\kappa > \frac{1}{6}$, nor for any quantum spin-liquid state.

The zero-temperature ground-state (GS) properties and phase diagram of a frustrated spin-1 $J_{1}$--$J_{2}$ Heisenberg model on the checkerboard square lattice are studied, using the coupled cluster method. We consider the case where the nearest-neighbour exchange bonds have strength $J_{1}>0$ and the next-nearest-neighbour exchange bonds present (viz., in the checkerboard pattern of the planar pyrochlore) have strength $J_{2} \equiv \kappa J_{1}>0$. We find significant differences from both the spin-1/2 and classical versions of the model. We find that the spin-1 model has a first phase transition at $\kappa_{c_{1}} \approx 1.00 \pm 0.01$ (as does the classical model at $\kappa_{{\rm cl}}=1$) between two antiferromagnetic phases, viz., a quasiclassical N\'{e}el phase (for $\kappa < \kappa_{c_{1}}$) and one of the infinitely degenerate family of quasiclassical phases (for $\kappa > \kappa_{c_{1}}$) that exists in the classical model for $\kappa > \kappa_{{\rm cl}}$, which is now chosen by the {\it order by disorder} mechanism as (probably) the "doubled N\'{e}el" (or N\'{e}el$^{\ast}$) state. By contrast, none of this family survives quantum fluctuations to form a stable GS phase in the spin-1/2 case. We also find evidence for a second quantum critical point at $\kappa_{c_{2}} \approx 2.0 \pm 0.5$ in the spin-1 model, such that for $\kappa > \kappa_{c_{2}}$ the quasiclassical (N\'{e}el$^{\ast}$) ordering melts and a nonclassical phase appears, which, on the basis of preliminary evidence, appears unlikely to have crossed-dimer valence-bond crystalline (CDVBC) ordering, as in the spin-1/2 case. Unlike in the spin-1/2 case, where the N\'{e}el and CDVBC phases are separated by a phase with plaquette valence-bond crystalline (PVBC) ordering, we find very preliminary evidence for such a PVBC state in the spin-1 model for all $\kappa > \kappa_{c_{2}}$.

Using the coupled cluster method (CCM) we study the full (zero-temperature) ground-state (GS) phase diagram of a spin-half ($s=1/2$) $J_{1}$-$J_{2}$ Heisenberg model on a cross-striped square lattice. Each site of the square lattice has 4 nearest-neighbour exchange bonds of strength $J_{1}$ and 2 next-nearest-neighbour (diagonal) bonds of strength $J_{2}$. The $J_{2}$ bonds are arranged so that the basic square plaquettes in alternating columns have either both or no $J_{2}$ bonds included. The classical ($s \rightarrow \infty$) version of the model has 4 collinear phases when $J_{1}$ and $J_{2}$ can take either sign. Three phases are antiferromagnetic (AFM), showing so-called N\'{e}el, double N\'{e}el and double columnar striped order respectively, while the fourth is ferromagnetic. For the quantum $s=1/2$ model we use the 3 classical AFM phases as CCM reference states, on top of which the multispin-flip configurations arising from quantum fluctuations are incorporated in a systematic truncation hierarchy. Calculations of the corresponding GS energy, magnetic order parameter and the susceptibilities of the states to various forms of valence-bond crystalline (VBC) order are thus carried out numerically to high orders of approximation and then extrapolated to the (exact) physical limit. We find that the $s=1/2$ model has 5 phases, which correspond to the four classical phases plus a new quantum phase with plaquette VBC order. The positions of the 5 quantum critical points are determined with high accuracy. While all 4 phase transitions in the classical model are first order, we find strong evidence that 3 of the 5 quantum phase transitions in the $s=1/2$ model are of continuous deconfined type.

The coupled cluster method (CCM) is used to study the zero-temperature properties of a frustrated spin-half ($s={1}{2}$) $J_{1}$--$J_{2}$ Heisenberg antiferromagnet (HAF) on a 2D chevron-square lattice. Each site on an underlying square lattice has 4 nearest-neighbor exchange bonds of strength $J_{1}>0$ and 2 next-nearest-neighbor (diagonal) bonds of strength $J_{2} \equiv x J_{1}>0$, with each square plaquette having only one diagonal bond. The diagonal bonds form a chevron pattern, and the model thus interpolates smoothly between 2D HAFs on the square ($x=0$) and triangular ($x=1$) lattices, and also extrapolates to disconnected 1D HAF chains ($x \to \infty$). The classical ($s \to \infty$) version of the model has N\'{e}el order for $0 < x < x_{{\rm cl}}$ and a form of spiral order for $x_{{\rm cl}} < x < \infty$, where $x_{{\rm cl}} = {1}{2}$. For the $s={1}{2}$ model we use both these classical states, as well as other collinear states not realized as classical ground-state (GS) phases, as CCM reference states, on top of which the multispin-flip configurations resulting from quantum fluctuations are incorporated in a systematic truncation scheme, which we carry out to high orders and extrapolate to the physical limit. We calculate the GS energy, GS magnetic order parameter, and the susceptibilities of the states to various forms of valence-bond crystalline (VBC) order, including plaquette and two different dimer forms. We find that the $s={1}{2}$ model has two quantum critical points, at $x_{c_{1}} \approx 0.72(1)$ and $x_{c_{2}} \approx 1.5(1)$, with N\'{e}el order for $0 < x < x_{c_{1}}$, a form of spiral order for $x_{c_{1}} < x < x_{c_{2}}$ that includes the correct three-sublattice $120^{\circ}$ spin ordering for the triangular-lattice HAF at $x=1$, and parallel-dimer VBC order for $x_{c_{2}} < x < \infty$.

Using the coupled cluster method we study the phase diagram of the spin-1/2 Heisenberg antiferromagnet on a honeycomb lattice with nearest-neighbor exchange coupling $J_{1}>0$ and frustrating next-nearest-neighbor coupling $J_{2} \equiv xJ_{1}>0$. In the range $0

We use the coupled cluster method to study the zero-temperature properties of an extended two-dimensional Heisenberg antiferromagnet formed from spin-1/2 moments on an infinite spatially anisotropic kagome lattice of corner-sharing isosceles triangles, with nearest-neighbor bonds only. The bonds have exchange constants $J_{1}>0$ along two of the three lattice directions and $J_{2} \equiv \kappa J_{1} > 0$ along the third. In the classical limit the ground-state (GS) phase for $\kappa < 1/2$ has collinear ferrimagnetic (N\'{e}el$'$) order where the $J_2$-coupled chain spins are ferromagnetically ordered in one direction with the remaining spins aligned in the opposite direction, while for $\kappa > 1/2$ there exists an infinite GS family of canted ferrimagnetic spin states, which are energetically degenerate. For the spin-1/2 case we find that quantum analogs of both these classical states continue to exist as stable GS phases in some regions of the anisotropy parameter $\kappa$, namely for $0<\kappa<\kappa_{c_1}$ for the N\'{e}el$'$ state and for (at least part of) the region $\kappa>\kappa_{c_2}$ for the canted phase. However, they are now separated by a paramagnetic phase without either sort of magnetic order in the region $\kappa_{c_1} < \kappa < \kappa_{c_2}$, which includes the isotropic kagome point $\kappa = 1$ where the stable GS phase is now believed to be a topological ($\mathbb{Z}_2$) spin liquid. Our best numerical estimates are $\kappa_{c_1} = 0.515 \pm 0.015$ and $\kappa_{c_2} = 1.82 \pm 0.03$.

We use the coupled cluster method in high orders of approximation to make a comprehensive study of the ground-state (GS) phase diagram of the spin-1/2 $J_{1}$--$J_{2}$--$J_{3}$ model on a two-dimensional honeycomb lattice with antiferromagnetic (AFM) interactions up to third-nearest neighbors. Results are presented for the GS energy and the average local on-site magnetization. With the nearest-neighbor coupling strength $J_{1} \equiv 1$ we find four magnetically ordered phases in the parameter window $J_{2},J_{3} \in [0,1]$, namely the N\'{e}el (N), striped (S), and anti-N\'{e}el (aN) collinear AFM phases, plus a spiral phase. The aN phase appears as a stable GS phase in the classical version of the model only for values $J_{3}<0$. Each of these four ordered phases shares a boundary with a disordered quantum paramagnetic (QP) phase, and at several widely separated points on the phase boundaries the QP phase has an infinite susceptibility to plaquette valence-bond crystalline order. We identify all of the phase boundaries with good precision in the parameter window studied, and we find three tricritical quantum critical points therein at: (a) $(J_{2}^{c_1},J_{3}^{c_1})=(0.51 \pm 0.01,0.69 \pm 0.01)$ between the N, S, and QP phases; (b) $(J_{2}^{c_2},J_{3}^{c_2})=(0.65 \pm 0.02,0.55 \pm 0.01)$ between the S, spiral, and QP phases; and (c) $(J_{2}^{c_3},J_{3}^{c_3})=(0.69 \pm 0.01,0.12 \pm 0.01)$ between the spiral, aN, and QP phases.

We study the ground-state (gs) phases of the spin-half anisotropic planar pyrochlore (or crossed chain) model using the coupled cluster method (CCM). The model is a frustrated antiferromagnetic (AFM) $J_{1}$--$J_{2}$ system on the checkerboard lattice, with nearest-neighbor exchange bonds $J_{1}>0$ and next-nearest-neighbor bonds $J_{2} \equiv \kappa J_{1} > 0$. Using various AFM classical ground states as CCM model states we present results for their gs energy, average on-site magnetization, and susceptibilities to plaquette valence-bond crystal (PVBC) and crossed-dimer valence-bond crystal (CDVBC) ordering. We show that the state with Neel ordering is the gs phase for $\kappa < \kappa_{c_1} \approx 0.80 \pm 0.01$, but that none of the fourfold set of AFM states selected by quantum fluctuations at $O(1/s)$ in a large-$s$ analysis (where $s$ is the spin quantum number) from the infinitely degenerate set of AFM states that form the gs phase for the classical version of the model (for $\kappa>1$) survives the quantum fluctuations to form a stable magnetically-ordered gs phase for the spin-half case. The Neel state becomes susceptible to PVBC ordering at or very near to $\kappa = \kappa_{c_1}$, and the fourfold AFM states become infinitely susceptible to PVBC ordering at $\kappa = \kappa_{c_2} \approx 1.22 \pm 0.02$. In turn, we find that these states become infinitely susceptible to CDVBC ordering for all values of $\kappa$ above a certain critical value at or very near to $\kappa = \kappa_{c_2}$. We thus find a Neel-ordered gs phase for $\kappa<\kappa_{c_1}$, a PVBC-ordered phase for $\kappa_{c_1} < \kappa < \kappa_{c_2}$, and a CDVBC-ordered phase for $\kappa > \kappa_{c_2}$. Both transitions are probably direct ones, although we cannot exclude very narrow coexistence regions confined to $0.79 \lesssim \kappa \lesssim 0.81$ and $1.20 \lesssim \kappa \lesssim 1.22$ respectively., Comment: 12 pages, 6 figures

We study the ground-state (gs) phase diagram of the frustrated spin-1/2 $J_{1}$--$J_{2}$ antiferromagnet with $J_{2}=\kappa J_1>0$ ($J_{1}>0$) on the honeycomb lattice, using the coupled-cluster method. We present results for the ground-state energy, magnetic order parameter and plaquette valence-bond crystal (PVBC) susceptibility. We find a paramagnetic PVBC phase for $\kappa_{c_1}<\kappa<\kappa_{c_2}$, where $\kappa_{c_1} \approx 0.207 \pm 0.003$ and $\kappa_{c_2} \approx 0.385 \pm 0.010$. The transition at $\kappa_{c_1}$ to the N\'{e}el phase seems to be a continuous deconfined transition (although we cannot exclude a very narrow intermediate phase in the range $0.21 \lesssim \kappa \lesssim 0.24$), while that at $\kappa_{c_2}$ is of first-order type to another quasiclassical antiferromagnetic phase that occurs in the classical version of the model only at the isolated and highly degenerate critical point $\kappa = 1/2$. The spiral phases that are present classically for all values $\kappa > 1/6$ are absent for all $\kappa \lesssim 1$., Comment: 6 pages, 5 figures

We study the ground-state (gs) properties of the frustrated spin-1/2 $J_{1}$--$J_{2}$--$J_{3}$ Heisenberg model on a honeycomb lattice with ferromagnetic (FM) nearest-neighbor ($J_{1}=-1$) exchange and frustrating antiferromagnetic (AFM) next-nearest-neighbor ($J_{2}>0$) and next-next-nearest-neighbor ($J_{3}>0$) exchanges, for the case $J_{3}=J_{2}$. We use the coupled cluster method in high orders of approximation, complemented by the exact diagonalization of a lattice with 32 sites, and calculate the gs energy, magnetic order parameter, and spin-spin correlation functions. We find a quantum phase transition between regions characterized by FM order and a form of AFM ("striped") collinear order at $J^{c}_{2} \approx 0.1095 \pm 0.0005$. We compare results for the FM case (with $J_{1}=-1$) to previous results for the corresponding AFM case (with $J_{1}=+1$). While the magnetic order parameters behave similarly for the FM and the AFM models for large values of the frustration parameter $J_{2}$, there are considerable differences between them for $J_{2}/|J_{1}| \lesssim 0.6$. For example, the quasiclassical collinear magnetic long-range order for the AFM model (with $J_{1}=+1$) breaks down at $J^{c_{2}}_{2} \approx 0.60$, whereas the "equivalent" point for the FM model (with $J_{1}=-1$) occurs at $J^{c}_{2} \approx 0.11$. Unlike in the AFM model (with $J_{1}=+1$), where a plaquette valence-bond crystal phase intrudes between the two corresponding quasiclassical AFM phases (with N\'eel and striped order) for $J^{c_{1}}_{2} < J_{2} < J^{c_{2}}_{2}$, with $J^{c_{1}}_{2} \approx 0.47$, we find no clear indications in the FM model for an intermediate magnetically disordered phase between the phases exhibiting FM and striped order. Instead, the evidence points strongly to a direct first-order transition between the two ordered phases of the FM model., Comment: 21 pages, 6 figures (a & b)

We study the ground-state (gs) phase diagram of the frustrated spin-1/2 $J_{1}$-$J_{2}$-$J_{3}$ antiferromagnet with $J_{2} = J_{3} =\kappa J_1$ on the honeycomb lattice, using coupled-cluster theory and exact diagonalization methods. We present results for the gs energy, magnetic order parameter, spin-spin correlation function, and plaquette valence-bond crystal (PVBC) susceptibility. We find a N\'eel antiferromagnetic (AFM) phase for $\kappa < \kappa_{c_{1}} \approx 0.47$, a collinear striped AFM phase for $\kappa > \kappa_{c_{2}} \approx 0.60$, and a paramagnetic PVBC phase for $\kappa_{c_{1}} \lesssim \kappa \lesssim \kappa_{c_{2}}$. The transition at $\kappa_{c_{2}}$ appears to be of first-order type, while that at $\kappa_{c_{1}}$ is continuous. Since the N\'eel and PVBC phases break different symmetries our results favor the deconfinement scenario for the transition at $\kappa_{c_{1}}$.

The coupled cluster method is applied to a spin-half model at zero temperature ($T=0$), which interpolates between Heisenberg antiferromagnets (HAF's) on a kagome and a square lattice. With respect to an underlying triangular lattice the strengths of the Heisenberg bonds joining the nearest-neighbor (NN) kagome sites are $J_{1} \geq 0$ along two of the equivalent directions and $J_{2} \geq 0$ along the third. Sites connected by $J_{2}$ bonds are themselves connected to the missing NN non-kagome sites of the triangular lattice by bonds of strength $J_{1}' \geq 0$. When $J_{1}'=J_{1}$ and $J_{2}=0$ the model reduces to the square-lattice HAF. The magnetic ordering of the system is investigated and its $T=0$ phase diagram discussed. Results for the kagome HAF limit are among the best available., Comment: 21 pages, 8 figures

We use the coupled cluster method (CCM) to study the zero-temperature phase diagram of a 2D frustrated spin-half antiferromagnet, the so-called Union Jack model. It is defined on a square lattice such that all nearest-neighbor bonds are present with a strength $J_{1} > 0$, but only half the next-nearest-neighbor bonds are present with a strength $J_{2} \equiv \kappa J_{1} > 0$. The bonds are arranged such that on the $2 \times 2$ unit cell they form the pattern of the Union Jack flag. We find strong evidence for a first phase transition between a N\'{e}el phase and a canted ferrimagnetic phase at a critical coupling $\kappa_{c_{1}} = 0.66 \pm 0.02$. At the transition the energy and its first derivative seem continuous, thus providing a typical scenario of a second-order transition, although a weakly first-order transition cannot be excluded. By contrast, the average on-site magnetization $M$ approaches a nonzero value $M_{c_{1}}=0.195 \pm 0.005$ on both sides of the transition, which is more typical of a first-order transition. The slope $dM/d\kappa$ also appears to be continuous, or very nearly so, at the critical point $\kappa_{c_{1}}$. We find strong evidence that the canted phase becomes unstable at large values of $\kappa$, and hence we have also used the CCM with a model collinear semi-stripe-ordered ferrimagnetic state in which alternating rows (and columns) are ferromagnetically and antiferromagnetically ordered. We find tentative evidence, based on the relative energies of the two states, for a second (first-order) phase transition between the canted and semi-stripe-ordered states at a large value of the coupling parameter around $\kappa_{c_{2}} \approx 125 \pm 5$. This prediction, however, is based on an extrapolation of the CCM results for the canted state into regimes where the CCM equations at any level of approximation beyond the lowest have no solutions., Comment: 31 pages, 8 figures

Using the coupled cluster method we study the zero-temperature phase diagram of a spin-half Heisenberg antiferromagnet (HAF), the so-called $J_{1}$--$J_{2}'$ model, defined on an anisotropic 2D lattice. With respect to an underlying square-lattice geometry the model contains antiferromagnetic ($J_{1} > 0$) bonds between nearest neighbors and competing ($J_{2}'>0$) bonds between next-nearest neighbors across only one of the diagonals of each square plaquette, the same diagonal in every square. Considered on an equivalent triangular-lattice geometry the model may be regarded as having two sorts of nearest-neighbor bonds, with $J_{2}' \equiv \kappa J_{1}$ bonds along parallel chains and $J_{1}$ bonds providing an interchain coupling. Hence, the model interpolates between a spin-half HAF on the square lattice at one extreme ($\kappa = 0$) and a set of decoupled spin-half chains at the other ($\kappa \to \infty$), with the spin-half HAF on the triangular lattice in between at $\kappa = 1$. We find strong evidence that quantum fluctuations favor a first-order transition from quasiclassical N\'{e}el order to a quantum helical state at a first critical point at $\kappa_{c_{1}} = 0.80 \pm 0.01$, by contrast with the corresponding second-order transition between the equivalent classical states at $\kappa_{{\rm cl}} = 0.5$. We also find strong evidence for a second critical point at $\kappa_{c_{2}} = 1.8 \pm 0.4$ where another first-order transition occurs, this time from the quantum helical phase to a collinear stripe-ordered phase. This latter result provides quantitative verification of a recent qualitative prediction of Starykh and Balents [Phys.\ Rev. Lett. {\bf 98}, 077205 (2007)] for the $J_{1}$--$J_{2}'$ model that did not, however, evaluate the corresponding critical point., Comment: 28 pages, 8 figures

We study the zero-temperature phase diagram of the $J_{1}^{XXZ}$--$J_{2}^{XXZ}$ Heisenberg model for spin-1 particles on an infinite square lattice interacting via nearest-neighbour ($J_1 \equiv 1$) and next-nearest-neighbour ($J_2 > 0$) bonds. Both bonds have the same $XXZ$-type anisotropy in spin space. The effects on the quasiclassical N\'{e}el-ordered and collinear stripe-ordered states of varying the anisotropy parameter $\Delta$ is investigated using the coupled cluster method carried out to high orders. By contrast with the spin-1/2 case studied previously, we predict no intermediate disordered phase between the N\'{e}el and collinear stripe phases, for any value of the frustration $J_2/J_1$, for either the $z$-aligned ($\Delta > 1$) or $xy$-planar-aligned ($0 \leq \Delta < 1$) states. The quantum phase transition is determined to be first-order for all values of $J_2/J_1$ and $\Delta$. The position of the phase boundary $J_{2}^{c}(\Delta)$ is determined accurately. It is observed to deviate most from its classical position $J_2^c = {1/2}$ (for all values of $\Delta > 0$) at the Heisenberg isotropic point ($\Delta = 1$), where $J_{2}^{c}(1) = 0.55 \pm 0.01$. By contrast, at the XY isotropic point ($\Delta = 0$), we find $J_{2}^{c}(0) = 0.50 \pm 0.01$. In the Ising limit ($\Delta \to \infty$) $J_2^c \to 0.5$ as expected., Comment: 20 pages, 5 figures

We report on a study of the dynamics of a magnetic antivortex in a submicron, asteroid shaped, permalloy ferromagnet using micromagnetic simulations. As with vortex states in disk and square geometries, a gyrotropic mode was found in which a shifted antivortex core orbits about the center of the asteroid. Pulsed magnetic fields were used to generate azimuthal or radial spin wave modes, depending on the field orientation. The degeneracy of low frequency azimuthal mode frequencies is lifted by gyrotropic motion of the antivortex core, and restored by inserting a hole in the center of the particle to suppress this motion. We briefly compare the dynamics of the vortex state of the asteroid to the antivortex. The size dependence of the antivortex modes is reported.

We develop a microscopic theory of the scattering, transmission, and sticking of 4He atoms impinging on a superfluid 4He slab at near normal incidence, and inelastic neutron scattering from the slab. The theory includes coupling between different modes and allows for inelastic processes. We find a number of essential aspects that must be observed in a physically meaningful and reliable theory of atom transmission and scattering; all are connected with multiparticle scattering, particularly the possibility of energy loss. These processes are (a) the coupling to low-lying (surface) excitations (ripplons/third sound) which is manifested in a finite imaginary part of the self energy, and (b) the reduction of the strength of the excitation in the maxon/roton region.