The antiferromagnetic Heisenberg model on the icosahedron presents unconventional properties at the classical and quantum level, which originate in the frustrated nature of the interactions between ...the spins. Here we examine the importance of the connectivity of the icosahedron for the appearance of a magnetization discontinuity as a function of an external field which separates two families of lowest energy configurations. We also investigate the transition from the classical to the quantum limit. The influence of connectivity on the magnetic properties is revealed by considering the cluster as being made up of a closed strip of a triangular lattice with two additional spins attached. The classical magnetization discontinuity is shown to evolve continuously from the discontinuity effected by these two spins when they are uncoupled to the cluster. In the second part the transition from the classical to the quantum limit is examined by focusing on the low energy spectrum, taking fully into account the spatial and the spin symmetry of the model in the characterization of the states. A symmetry analysis of the highly degenerate lowest energy classical manifold identifies as its direct fingerprint the low energy quantum states for spin magnitude as low as s = 1, with the latter following a tower of states behavior which relates to the icosahedron having a structure reminiscent of a depleted triangular lattice. The classical character of the AHM for small s is also detected on the ground state energy and correlation functions. On the other hand the classical magnetization discontinuity in a field eventually disappears for small s, after a weak reentrant behavior.
The classical ground state magnetic response of fullerene molecules that resemble capped carbon nanotubes is calculated within the framework of the antiferromagnetic Heisenberg model. It is found ...that the magnetic response depends subtly on spatial symmetry and chirality. Clusters based on armchair carbon nanotubes which are capped with non-neighboring pentagons and have D
spatial symmetry have a number of magnetization discontinuities which increases with their size. This occurs even though the model completely lacks magnetic anisotropy, and even though the only source of frustration are the two groups of six pentagons located at the ends of the molecules, which become more strongly outnumbered as the clusters are filled in the middle with more unfrustrated hexagons with increasing size. For the cluster with 180 vertices there are already seven magnetization and one susceptibility discontinuities. Contrary to that, similar molecules which have D
spatial symmetry reach a limit of one magnetization and two susceptibility ground state discontinuities, while fullerene molecules based on zigzag carbon nanotubes and capped by neighboring pentagons also reach a fixed number of discontinuities with increasing size.
The icosahedron has a ground state magnetization discontinuity in an external magnetic field when classical spins mounted on its vertices are coupled according to the antiferromagnetic Heisenberg ...model. This is so even if there is no magnetic anisotropy in the Hamiltonian. The discontinuity is a consequence of the frustrated nature of the interactions, which originates in the topology of the cluster. Here it is found that the addition of the next order isotropic spin exchange interaction term in the Hamiltonian, the biquadratic exchange interaction, significantly enriches the classical ground state magnetic response. For relatively weak biquadratic interaction new discontinuities emerge, while for even stronger the number of discontinuities for this small molecule can go up to seven, accompanied by a susceptibility discontinuity. These results demonstrate the possibility of using a small entity like the icosahedron as a magnetic unit whose ground state spin configuration and magnetization can be tuned between many different non-overlapping regimes with the application of an external field.
The antiferromagnetic Heisenberg model on the dodecahedron possesses a number of ground state magnetization discontinuities in a field at the classical and quantum level, even though it lacks ...magnetic anisotropy. Here the model is considered for two dodecahedra coupled antiferromagnetically along one of their faces, as a first step to determine the magnetic response of collections of fullerene molecules. The magnetic response is determined from the competition among the intra-, interdodecahedral exchange and magnetic field energies. At the classical level the discontinuities of the isolated dodecahedron are renormalized by the interdodecahedral coupling, while new ones show up, with the maximum number of ground state discontinuities being six for a specific range of the coupling. In the full quantum limit where the individual spin magnitude , there are two ground state discontinuities originating in the single discontinuity of the isolated dodecahedron, and another one due to the intermolecular coupling, generating a total of three discontinuities which come one right after the other. These results show that the magnetic response of more than one dodecahedra interacting together is quite richer than the one of a single dodecahedron.
We present a detailed study of the fidelity, the entanglement entropy and the entanglement spectrum, for a dimerized chain of spinless fermions-a simplified Su-Schrieffer-Heeger (SSH) model-with open ...boundary conditions which is a well-known example for a model supporting a symmetry protected topological (SPT) phase. In the non-interacting case the Hamiltonian matrix is tridiagonal and the eigenvalues and vectors can be given explicitly as a function of a single parameter which is known analytically for odd chain lengths and can be determined numerically in the even length case. From a scaling analysis of these data for essentially semi-infinite chains we obtain the fidelity susceptibility and show that it contains a boundary contribution which is different in the topologically ordered than in the topologically trivial phase. For the entanglement spectrum and entropy we confirm predictions from massive field theory for a block in the middle of an infinite chain but also consider blocks containing the edge of the chain. For the latter case we show that in the SPT phase additional entanglement-as compared to the trivial phase-is present which is localized at the boundary. Finally, we extend our study to the dimerized chain with a nearest-neighbour interaction using exact diagonalization, Arnoldi and density-matrix renormalization group methods and show that a phase transition into a topologically trivial charge-density wave phase occurs.
Thermalization is investigated for the one-dimensional anisotropic antiferromagnetic Heisenberg model with dimerized nearest-neighbor interactions that break integrability. For this purpose the time ...evolution of local operator expectation values after an interacting quench is calculated directly with the Chebyshev polynomial expansion, and the deviation of the diagonal from the canonical thermal ensemble value is calculated for increasing system size for these operators. The spatial and spin symmetries of the Hamiltonian are taken into account to divide it into symmetry subsectors. The rate of thermalization is found to weaken with the dimerization parameter as the Hamiltonian evolves between two integrable limits, the non-dimerized and the fully dimerized where the chain breaks up into isolated dimers. This conclusion is supported by the distribution of the local operator off-diagonal elements between the eigenstates of the Hamiltonian with respect to their energy difference, which determines the strength of temporal fluctuations. The off-diagonal elements have a low-energy peak for small dimerization which facilitates thermalization, and originates in the reduction of spatial symmetry with respect to the non-dimerized limit. For increasing dimerization their distribution changes and develops a single low-energy maximum that relates to the fully dimerized limit and slows down thermalization.
•The classical and s=1/2 ground-state magnetization of fullerene molecules is found.•Frustration results in classical magnetization and susceptibility discontinuities.•The number of classical ...discontinuities can go up to 6 for a single molecule.•For several molecules the classical zero-field ground state has finite magnetization.•The molecule with 34 sites has a doubly-degenerate ground state for spins s=1/2.
The ground-state magnetic response of fullerene molecules with up to 36 vertices is calculated, when spins classical or with magnitude s=12 are located on their vertices and interact according to the nearest-neighbor antiferromagnetic Heisenberg model. The frustrated topology, which originates in the pentagons of the fullerenes and is enhanced by their close proximity, leads to a significant number of classical magnetization and susceptibility discontinuities, something not expected for a model lacking magnetic anisotropy. This establishes the classical discontinuities as a generic feature of fullerene molecules irrespective of their symmetry. The largest number of discontinuities have the molecule with 26 sites, four of the magnetization and two of the susceptibility, and an isomer with 34 sites, which has three each. In addition, for several of the fullerenes the classical zero-field lowest energy configuration has finite magnetization, which is unexpected for antiferromagnetic interactions between an even number of spins and with each spin having the same number of nearest-neighbors. The molecules come in different symmetries and topologies and there are only a few patterns of magnetic behavior that can be detected from such a small sample of relatively small fullerenes. Contrary to the classical case, in the full quantum limit s=12 there are no discontinuities for a subset of the molecules that was considered. This leaves the icosahedral symmetry fullerenes as the only ones known supporting ground-state magnetization discontinuities for s=12. It is also found that a molecule with 34 sites has a doubly-degenerate ground state when s=12.
It is shown that in antiferromagnetic open or closed corrals of magnetic adatoms grown on surfaces, the attachment of a single extra adatom anywhere in the corral impacts on the geometrical topology ...of the nanosystem and generates complex magnetic structures when a magnetic field is applied or a magnetic coupling to a ferromagnetic substrate exists. The spin configuration of the corral can be tuned to a nonplanar state or a planar noncollinear or ferrimagnetic state by adjusting its number of sites, the location of the extra adatom, or the strength of the coupling to the ferromagnetic substrate. This shows the possibility to generate nontrivial magnetic textures with atom-by-atom engineering anywhere in the corral and not only at the edges.
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