Roman Rausch, Matthias Peschke, Cassian Plorin, Jürgen Schnack, Christoph Karrasch
SciPost Phys. 14, 052 (2023) ·
published 28 March 2023

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The ferrimagnetic phase of the sawtooth chain with mixed ferromagnetic nearestneighbour interactions $J$ and antiferromagnetic nextnearestneighbour interactions $J'$ (within the isotropic Heisenberg model) was previously characterized as a phase with commensurate order. In this paper, we demonstrate that the system in fact exhibits an incommensurate quantum spin spiral. Even though the ground state is translationally invariant in terms of the local spin expectations $\left<{\vec{S}_i}\right>$, the spiral can be detected via the connected spinspin correlations $\left<{\vec{S}_i\cdot\vec{S}_j}\right>\left<{\vec{S}_i}\right>\cdot\left<{\vec{S}_j}\right>$ between the apical spins. It has a long wavelength that grows with $J'$ and that soon exceeds finitesystem sizes typically employed in numerical simulations. A faithful treatment thus requires the use of stateoftheart simulations for large, periodic systems. In this work, we are able to accurately treat up to $L=400$ sites (200 unit cells) with periodic boundary conditions using the densitymatrix renormaliztion group (DMRG). Exploiting the SU(2) symmetry allows us to directly compute the lowestenergy state for a given total spin. Our results are corroborated by variational uniform matrix product state (VUMPS) calculations, which work directly in the thermodynamic limit at the cost of a lower accuracy.
Roman Rausch, Matthias Peschke, Cassian Plorin, Christoph Karrasch
SciPost Phys. 12, 143 (2022) ·
published 2 May 2022

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We compute groundstate properties of the isotropic, antiferromagnetic Heisenberg model on the sodalite cage geometry. This is a 60spin spherical molecule with 24 vertexsharing tetrahedra which can be regarded as a molecular analogue of a capped kagome lattice and which has been synthesized with highspin rareearth atoms. Here, we focus on the $S=1/2$ case where quantum effects are strongest. We employ the SU(2)symmetric densitymatrix renormalization group (DMRG). We find a threefold degenerate ground state that breaks the spatial symmetry and that splits up the molecule into three large parts which are almost decoupled from each other. This stands in sharp contrast to the behaviour of most known spherical molecules. On a methodological level, the disconnection leads to ``glassy dynamics'' within the DMRG that cannot be targeted via standard techniques. In the presence of finite magnetic fields, we find broad magnetization plateaus at 4/5, 3/5, and 1/5 of the saturation, which one can understand in terms of localized magnons, singlets, and doublets which are again nearly decoupled from each other. At the saturation field, the zeropoint entropy is $S=\ln(182)\approx 5.2$ in units of the Boltzmann constant.
SciPost Phys. 10, 087 (2021) ·
published 23 April 2021

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We solve the quantummechanical antiferromagnetic Heisenberg model with spins positioned on vertices of the truncated icosahedron using the densitymatrix renormalization group (DMRG). This describes magnetic properties of the undoped C$_{60}$ fullerene at half filling in the limit of strong onsite interaction $U$. We calculate the ground state and correlation functions for all possible distances, the lowest singlet and triplet excited states, as well as thermodynamic properties, namely the specific heat and spin susceptibility. We find that unlike smaller C$_{20}$ or C$_{32}$ that are solvable by exact diagonalization, the lowest excited state is a triplet rather than a singlet, indicating a reduced frustration due to the presence of many hexagon faces and the separation of the pentagonal faces, similar to what is found for the truncated tetrahedron. This implies that frustration may be tuneable within the fullerenes by changing their size. The spinspin correlations are much stronger along the hexagon bonds and exponentially decrease with distance, so that the molecule is large enough not to be correlated across its whole extent. The specific heat shows a hightemperature peak and a lowtemperature shoulder reminiscent of the kagomé lattice, while the spin susceptibility shows a single broad peak and is very close to the one of C$_{20}$.