B. Harris, M. A. Kastner, I. Using the Wigner-Eckart theorem one can prove that the part of the Sz-operator that couples to |Sm+1,Sm⟩ states is actually related to the action of S+, and the following relation holds. U. Schollwöck, S. Todo, S. Trebst, M. Troyer, P. Werner, and S. Wessel. Since our calculations were done on finite clusters, one must be careful interpreting results at fields very close to saturation, which might be obtained from small Hilbert spaces with only one or two flipped spins. The upper x-axes shown in Figs. Our approach of using this magnetization curve to compare spin-wave results with numerical simulations is thus justified. , we note that the singlet excitation is also characterized by a 20-site ring with altered correlations, albeit differently positioned. the specific heat per site (or per spin): and the zero-field uniform magnetic susceptibility. Jiang and Kivelson solved the model on   . To get an idea of the variability of the extrapolations, fits at magnetizations m=0, 1/8, and 1/4 are shown in Fig. Data from bigger clusters suggests that these low-lying excitations form a continuum. (3)] is exactly satisfied for all magnetizations. It is therefore not surprising that the classical dispersion is almost identical to our exact results in the vicinity of these polarizations. F. C. Coomer, V. Bondah-Jagalu, K. J. . The spin-spin correlations in the ground state can be determined very accurately using DMRG and indicate that the molecule is large enough not to be fully correlated across its full extent. This Taking into account translation symmetries, the Hilbert space for a cluster of N sites at magnetization m encompasses roughly (NN/2−mN)/N states. The almost linear decrease at high fields however is due to the canting of the spins and has nothing to do with fluctuations because the exact result is almost identical to the classical curve. However, they discussed very different questions; and we further present results for the lowest excited states as well as thermodynamics. The former has only triangular plaquettes, the latter only pentagonal ones, and both are small enough to be solved exactly by full diagonalization if spatial symmetries are exploited to reduce the Hilbert space size  . The location of the distinct pole at k=X thus no longer scales to zero in the thermodynamic limit, but is simply equal the magnetic field. [■] Previous results at zero field are taken from Ref. With increasing magnetization, the weights of the magnon poles decrease, while at the same time, poles at higher energies become more important. (4) and determine c from the fitting parameters. 4-6 and 9 represent the linear spin-wave mapping between the magnetization m and the magnetic field h, as a function of which spin-wave results are unambiguous. IV. IV, the main part of this work, we present our results for the dynamical spin correlation functions obtained by exact diagonalizations of clusters with up to 64 sites. Manson, M. M. Conner, F. Xiao, C. P. Landee, F. A. Chaves, S. Soriano, M. A. [■] zhitomirsky99, , where the decay into two spin waves sets in in the vicinity of the gapless point. T. Lancaster, S. J. Blundell, M. L. Brooks, P. J. Baker, F. L. Pratt, J. L. However, the latter has a much smaller singlet-triplet gap of and a very small neutral gap of   [■] The strong intensity reflects the dominantly antiferromagnetic character of the spin alignment. For polarizations close to the ferromagnetic regime, the number of poles decreases rapidly. Based on these results, we can say that high energy magnons around (π,π) become unstable at a critical polarization mc≈0.3. The σ model description is valid at small fields, where the staggered moment ms is large. [■] System class. III.5), and the staggered moment ms (Sect. At zero field, it is well known that the dispersion obtained within lowest-order spin-wave theory is renormalized by quantum fluctuations, leading to energies roughly 16% higher than this simplest prediction. Other authors have argued that there should only be a quantitative difference  However, due to sharp distributions we are still able to distinguish the different bonds (see Fig. igarashi92, ; sandvik97, , these microscopic parameters also depend significantly on the strength of the magnetic field. This density matrix is again purified into a state vector, but all operators act on the physical sites only, so that the additional “ancilla” cites are automatically traced over when taking expectation values using the state . [■] As an exception to this rule, the pole at X=(π,π) in the longitudinal structure factor originates from the lowest-lying spin S=Sz+1 level, as can be seen in Fig. [■] [■] , as well as for smaller fullerene geometries  The second mode now has a gap proportional to the magnetic field. This situation has changed with the synthesis of CuBr4 and CuCl4 compounds woodward02 ; lancaster07 ; coomer07 that have experimentally accessible saturation fields of less than 25 Tesla. [■] In Fig. The S+ scattering operator entering S−+ couples only to total spin S=Sm+1 states in the spectrum because it is the +1 component of a spin 1 tensor operator. The specific position of the 20-site ring must be due to our mapping choice to a chain. with α,β=x,y,z,+,−, is the Fourier transformation of the equal-time spin-spin correlators and can be directly measured in elastic neutron scattering. Erwin, M. Greven, A. Inspecting the longitudinal structure factor at (3π/4,3π/4) for instance, or equivalently, the transverse spin correlations at (π/4,π/4), we see that the spin-wave band fades away at m≈0.3 and enters a continuum, which on these finite clusters manifests itself as an area with densely distributed poles having relatively small intensity.

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