Triplon mean-field analysis of an antiferromagnet with degenerate Shastry-Sutherland ground states

We look into the quantum phase diagram of a spin-$\frac{1}{2}$ antiferromagnet on the square lattice with degenerate Shastry-Sutherland ground states, for which only a schematic phase diagram is known so far. Many exotic phases were proposed in the schematic phase diagram by the use of exact diagonalization on very small system sizes. In our present work, an important extension of this antiferromagnet is introduced and investigated in the thermodynamic limit using triplon mean-field theory. Remarkably, this antiferromagnet shows a stable plaquette spin-gapped phase like the original Shastry-Sutherland antiferromagnet, although both of these antiferromagnets differ in the Hamiltonian construction and ground state degeneracy. We propose a sublattice columnar dimer phase which is stabilized by the second and third neighbor antiferromagnetic Heisenberg exchange interactions. There are also some commensurate and incommensurate magnetically ordered phases, and other spin-gapped phases which find their places in the quantum phase diagram. Mean-field results suggest that there is always a level-crossing phase transition between two spin gapped phases, whereas in other situations, either a level-crossing or a continuous phase transition happens

Absence of magnetic order for the spin-half Heisenberg antiferromagnet on the star lattice

We study the ground-state properties of the spin-half Heisenberg antiferromagnet on the two-dimensional star lattice by spin-wave theory, exact diagonalization and a variational mean-field approach. We find evidence that the star lattice is (besides the \kagome lattice) a second candidate among the 11 uniform Archimedean lattices where quantum fluctuations in combination with frustration lead to a quantum paramagnetic ground state. Although the classical ground state of the Heisenberg antiferromagnet on the star exhibits a huge non-trivial degeneracy like on the \kagome lattice, its quantum ground state is most likely dimerized with a gap to all excitations. Finally, we find several candidates for plateaux in the magnetization curve as well as a macroscopic magnetization jump to saturation due to independent localized magnon states.Comment: new extended version (6 pages, 6 figures) as published in Physical Review

Spin Waves in Quantum Antiferromagnets

Using a self-consistent mean-field theory for the $S=1/2$ Heisenberg antiferromagnet Kr\"uger and Schuck recently derived an analytic expression for the dispersion. It is exact in one dimension ($d=1$) and agrees well with numerical results in $d=2$. With an expansion in powers of the inverse coordination number $1/Z$ ($Z=2d$) we investigate if this expression can be {\em exact} for all $d$. The projection method of Mori-Zwanzig is used for the {\em dynamical} spin susceptibility. We find that the expression of Kr\"uger and Schuck deviates in order $1/Z^2$ from our rigorous result. Our method is generalised to arbitrary spin $S$ and to models with easy-axis anisotropy \D. It can be systematically improved to higher orders in $1/Z$. We clarify its relation to the $1/S$ expansion.Comment: 8 pages, uuencoded compressed PS-file, accepted as Euro. Phys. Lette

From bcc to fcc: interplay between oscillating long-range and repulsive short-range forces

This paper supplements and partly extends an earlier publication, Phys. Rev. Lett. 95, 265501 (2005). In $d$-dimensional continuous space we describe the infinite volume ground state configurations (GSCs) of pair interactions \vfi and \vfi+\psi, where \vfi is the inverse Fourier transform of a nonnegative function vanishing outside the sphere of radius $K_0$, and $\psi$ is any nonnegative finite-range interaction of range $r_0\leq\gamma_d/K_0$, where $\gamma_3=\sqrt{6}\pi$. In three dimensions the decay of \vfi can be as slow as $\sim r^{-2}$, and an interaction of asymptotic form $\sim\cos(K_0r+\pi/2)/r^3$ is among the examples. At a dimension-dependent density $\rho_d$ the ground state of \vfi is a unique Bravais lattice, and for higher densities it is continuously degenerate: any union of Bravais lattices whose reciprocal lattice vectors are not shorter than $K_0$ is a GSC. Adding $\psi$ decreases the ground state degeneracy which, nonetheless, remains continuous in the open interval $(\rho_d,\rho_d')$, where $\rho_d'$ is the close-packing density of hard balls of diameter $r_0$. The ground state is unique at both ends of the interval. In three dimensions this unique GSC is the bcc lattice at $\rho_3$ and the fcc lattice at $\rho_3'=\sqrt{2}/r_0^3$.Comment: Published versio

Relativistic electronic dressing

We study the effects of the relativistic electronic dressing in laser-assisted electron-hydrogen atom elastic collisions. We begin by considering the case when no radiation is present. This is necessary in order to check the consistency of our calculations and we then carry out the calculations using the relativistic Dirac-Volkov states. It turns out that a simple formal analogy links the analytical expressions of the differential cross section without laser and the differential cross section in presence of a laser field.Comment: 11 pages, 18 figures, Late

More Benefits of Semileptonic Rare B Decays at Low Recoil: CP Violation

We present a systematic analysis of the angular distribution of Bbar -> Kbar^\ast (-> Kbar pi) l^+ l^- decays with l = e, mu in the low recoil region (i.e. at high dilepton invariant masses of the order of the mass of the b-quark) to account model-independently for CP violation beyond the Standard Model, working to next-to-leading order QCD. From the employed heavy quark effective theory framework we identify the key CP observables with reduced hadronic uncertainties. Since some of the CP asymmetries are CP-odd they can be measured without B-flavour tagging. This is particularly beneficial for Bbar_s,B_s -> phi(-> K^+ K^-) l^+ l^- decays, which are not self-tagging, and we work out the corresponding time-integrated CP asymmetries. Presently available experimental constraints allow the proposed CP asymmetries to be sizeable, up to values of the order ~ 0.2, while the corresponding Standard Model values receive a strong parametric suppression at the level of O(10^-4). Furthermore, we work out the allowed ranges of the short-distance (Wilson) coefficients C_9,C_10 in the presence of CP violation beyond the Standard Model but no further Dirac structures. We find the Bbar_s -> mu^+ mu^- branching ratio to be below 9*10^-9 (at 95% CL). Possibilities to check the performance of the theoretical low recoil framework are pointed out.Comment: 18 pages, 3 fig.; 1 reference and comment on higher order effects added; EOS link fixed. Minor adjustments to Eqs 4.1-4.3 to match the (lower) q^2-cut as given in paper. Main results and conclusions unchanged; v3+v4: treatment of exp. uncert. in likelihood-function in EOS fixed and constraints from scan on C9,C10 updated (Fig 2,3 and Eqs 3.2,3.3). Main results and conclusions absolutely unchange

The Benefits of B ---> K* l+ l- Decays at Low Recoil

Using the heavy quark effective theory framework put forward by Grinstein and Pirjol we work out predictions for B -> K* l+ l-, l = (e, mu), decays for a softly recoiling K*, i.e., for large dilepton masses sqrt{q^2} of the order of the b-quark mass m_b. We work to lowest order in Lambda/Q, where Q = (m_b, sqrt{q^2}) and include the next-to-leading order corrections from the charm quark mass m_c and the strong coupling at O(m_c^2/Q^2, alpha_s). The leading Lambda/m_b corrections are parametrically suppressed. The improved Isgur-Wise form factor relations correlate the B -> K* l+ l- transversity amplitudes, which simplifies the description of the various decay observables and provides opportunities for the extraction of the electroweak short distance couplings. We propose new angular observables which have very small hadronic uncertainties. We exploit existing data on B -> K* l+ l- distributions and show that the low recoil region provides powerful additional information to the large recoil one. We find disjoint best-fit solutions, which include the Standard Model, but also beyond-the-Standard Model ones. This ambiguity can be accessed with future precision measurements.Comment: 31 pages, 8 figures; Instability near minimal recoil from numerics removed, Fig. 1 replaced and minor shifts in short distance uncertainties in SM predictions; typos corrected and references added; main results and conclusions unchange

Effective interactions between star polymers

We study numerically the effective pair potential between star polymers with equal arm lengths and equal number $f$ of arms. The simulations were done for the soft core Domb-Joyce model on the simple cubic lattice, to minimize corrections to scaling and to allow for an unlimited number of arms. For the sampling, we used the pruned-enriched Rosenbluth method (PERM). We find that the potential is much less soft than claimed in previous papers, in particular for $f\gg 1$. While we verify the logarithmic divergence of $V(r)$, with $r$ being the distance between the two cores, predicted by Witten and Pincus, we find for $f>20$ that the Mayer function is hardly distinguishable from that for a Gaussian potential.Comment: 5 pages, 5 figure