A frustrated spin system is still quite challenging for a theoretical description. IV. 9. The zero-energy mode of the longitudinal structure factor at momentum (0,0) is proportional to the magnetization squared, i.e., Szz(ω=0,q=Γ)=(Sz)2. the specific heat per site (or per spin): and the zero-field uniform magnetic susceptibility. Alternatively, ms can be obtained from the transverse structure factor as, where N′ is a normalization factor. Y. J. Kim, A. Aharony, R. J. Birgeneau, F. C. Chou, O. Entin-Wohlman, R. W. Within linear spin-wave approximation, magnons are stable at any momentum and magnetic field, simply because the Hamiltonian does not contain terms that would allow a single magnon to decay into two spin waves. JP18F18750. 38, D-01187 Dresden, Germany. For example, the infamous sign problem  13 thus represent nothing but the inverse magnetization curve m(h). get: © Copyright 2012, Ivan Gonzalez. For , we can expect that the fullerene properties approach those of a hexagonal lattice. This interpretation is consistent with the observed overestimation of almost a factor 3/2. Looking at the spin-spin correlations in the excited state in Fig. Rather than focussing on a particular feature, we aim to give an overview of the various properties induced by the coupling to the magnetic field. For the next-nearest neighbours (distance ), there are also two types of bonds (see Fig. Furthermore, we note that all the pentagon faces are completely separated by the hexagons, so that all regions with adjacent frustrated pentagons are broken up in . state energy and wavefunction. ): two PP-bonds by going along the P-bonds twice, ending up in the same-face pentagon of a given vertex; and four HP-bonds, by going along H and P (in any order), ending up in the same-face hexagon. There are two ways to extract the spin-wave velocity c from exact diagonalization results: One can either determine the slope of the dispersion in the vicinity of the ground state momentum, or, one can fit the finite-size scaling of the ground state energy to Eq. where |q−Q|≪1 and c is the spin-wave velocity. 2 for the location of the momenta in different clusters, and thus still far from the cone center. The spin-wave result has been derived in Ref. III.5), and the staggered moment ms (Sect. 11 with Fig. The result for is shown in Fig. B. Harris, M. A. Kastner, I. Heisenberg antiferromagnetic model. . pentagon faces. Combined with the Lehmann representation. (5) gives a very good result at zero field schulz96 ; richter04 , it considerably underestimates the staggered moment at small fields. (1)]. We note that the linear spin-wave approximation captures these effects extremely well and is in perfect agreement with Monte-Carlo data. For higher magnetizations, the region of instability quickly increases. (3)] is exactly satisfied for all magnetizations. We can thus construct a susceptibility tensor as, Defining the terms parallel and perpendicular with respect to the direction of the staggered moment, the transverse susceptibility χ⊥ measures the variation of the uniform magnetization with respect to the applied field. It can be interpreted in a similar way, the difference being that singlet states do not contribute anymore. For , the distance is larger than the most distant site in the same-face hexagon. [■] We shall call them “hexagon bonds” (H-bonds) and “pentagon bonds” (P-bonds). The antiferromagnetic spin-12 Heisenberg model on the square lattice has been investigated in great detail over the past two decades, primarily because the parent compounds of superconducting copper-oxide materials are well described by this model manousakis91 ; barnes91 . L. Gamper, E. Gull, S. Gürtler, A. Honecker, R. Igarashi, M. Körner, The specific heat shows a high-temperature Moreover, the geometry has an interesting connection to the problem of frustrated spin systems. Fig. The magnetization curve of the Heisenberg model has been calculated before by exact diagonalizations of clusters containing at least 40 sites richter04 and also quantum Monte-Carlo simulations sandvik99b ; richter04 . where is the magnetization at a given external field strength and the Hamiltonian is changed to , with the total spin : While the specific heat can be exactly calculated using the squared Hamiltonian average , in practice this becomes quite expensive at every -step, so that we use a numerical differentiation of with spline interpolation instead. The aim of the present work is to provide a comprehensive numerical study of the Heisenberg antiferromagnet in magnetic fields ranging from zero up to saturation. 0:56 and a VBS phase for 0:56 . The truncated icosahedron is part of the icosahedral group , whose other members are the icosahedron with 12 sites and the dodecahedron with 20 sites (which is also the smallest fullerene )  4 of Ref. . The staggered magnetization behaves as neuberger89 ; sandvik97. Another open question is whether the frustrated pentagons can still measurably affect any properties of in the large- limit. Realigning the tower in the presence of a magnetic field is thus equivalent to shifting the spin lowering and raising contributions to the transverse structure factors in such a way that the lowest-lying poles of the k=Q modes coincide. Ya. system Hamiltonian to the antiferromagnetic Heisenberg model. Hence, it is useful to define a transverse component Sxy as. ). J 2 0:61. In principle, it is possible to calculate ρs in exact diagonalizations einarsson95 , but it is far easier and more accurate to obtain the spin-stiffness from quantum Monte-Carlo simulations as the global winding number fluctuations pollock84 . due to its finite and very manageable amount of sites. Comparisons with spin-wave calculations are established by mapping the magnetic field h onto m via the inverse magnetization curve h(m) obtained within linear spin-wave theory. . On the square lattice, and more generally on any sufficiently connected bipartite lattice, the model is magnetically ordered at zero temperature and the long-wavelength properties such as the magnetic order vaknin87 , the low-energy excitations coldea01 or the temperature dependence of the magnetic correlations birgeneau99 ; elstner95 ; cuccoli97 are well described within a semiclassical setting anderson52 ; oguchi60 ; chakravarty89 . 9, we show the staggered magnetization obtained from extrapolations based on Eq. In exact diagonalizations, the restriction to relatively small systems makes it difficult to extract wave vector dependent quantities to the thermodynamic limit. [■] 7(a). , simulated by the Heisenberg model. this: See a full implementation of the above code. IV. In contrast, our field dependent results at (π/2,π/2) [and to a lesser extent also (π,0)] reveal a large negative slope, not at all compatible with the flat linear spin-wave results.


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