a squared fraction of Clebsch-Gordan coefficients. Again, the Hamiltonian that we will build is the antiferromagnetic Heisenberg The dodecahedron has two peaks. Combined with the Lehmann representation. This implies that frustration may be tuneable within the Looking at the decay of the correlations with distance, we find when an exponential fit is applied to the maximal absolute values (previously, was proposed  This interpretation is consistent with the observed overestimation of almost a factor 3/2. The top panel shows the spectrum of the Hamiltonian without magnetic field, while in the bottom panel, we have subtracted the contribution hSz, for a magnetic field h corresponding to m=1/4, i.e., Sz=8 on this cluster. we have and . The antiferromagnetic spin-1 2 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 . Away from the special (π,π)-point, our results are much clearer and show evidence for the decay of spin waves in multi spin-wave continua. The strong intensity reflects the dominantly antiferromagnetic character of the spin alignment. The validity of the hydrodynamic relation in a magnetic field has been confirmed very recently in Ref. This allows to grow the bond dimension dynamically, until it becomes prohibitively large, at which point we switch to the faster 1-site algorithm (typically around ). , we see that the H-bonds are weakened ( to ), while the P-bonds are strengthened ( to ) along the 20-site ring as compared to the rest of the system. [■] To get an idea of the variability of the extrapolations, fits at magnetizations m=0, 1/8, and 1/4 are shown in Fig. Manson, M. M. Conner, F. Xiao, C. P. Landee, F. A. Chaves, S. Soriano, M. A. icosahedron: , dodecahedron: ) turns out to be significantly larger than the singlet-triplet gap (cf. Thus, we can average over the respective bonds and take the resulting distribution width as a measure of error, with a -distribution expected in the limit of . . This is the finite-size manifestation of the magnon instability predicted in Ref. After this overview, let us now look at some of the discovered features in more detail, using the exact dynamical structure factors without any interpolation presented in Fig. Similarly, one can show that S+− contains a shadow of Szz which is generically Clebsch-Gordan suppressed at large m and N. We have seen that the location of the dominant pole in the longitudinal structure factor at momentum (π,π), and hence at (0,0) in the transverse spin correlations, is equal to the magnetic field. The specific heat shows a high-temperature frustration due to the presence of many hexagon faces and the separation of the The correlations along the bonds turn out to be nonetheless very different as a consequence of geometry, as will be seen below. 9. With these optimizations, the ground state can be found quite efficiently and we can take the variance per site. In addition to being renormalized by quantum fluctuations, see, e. g., Refs. [■] It would be interesting to investigate these subtle differences in more detail and compare the predications of these two numerical approaches to more advanced spin-wave calculations zhitomirsky99 . For small fields, the spins preferably align antiferromagnetically in the plane perpendicular to the magnetic field, with a small uniform out-of-plane component, as depicted in Fig. Along the diagonal, one finds α=−7/3+2/√1−h2, which changes sign at a critical field hc=2/√7hs ≈0.755 hs, corresponding to a magnetization mc≈0.33. At zero field, the structure factors reflect the antiferromagnetic order with a pronounced peak at X=(π,π). The elastic energy required to twist a spin arrangement is proportional to the spin-stiffness ρs, see Eq. ), and recognize that the value indeed slowly approaches the one for the hexagonal lattice   The energy per spin is found to be .

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