The antiferromagnetic $S=1/2$ Heisenberg model on the ${\text{C}}_{60}$ fullerene geometry

Abstract

We solve the quantum-mechanical antiferromagnetic Heisenberg model with spins positioned on vertices of the truncated icosahedron using the density-matrix renormalization group (DMRG). This describes magnetic properties of the undoped C${}_{60}$ fullerene at half filling in the limit of strong on-site 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 spin-spin 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 high-temperature peak and a low-temperature shoulder reminiscent of the kagome lattice, while the spin susceptibility shows a single broad peak and is very close to the one of C${}_{20}$.

arXiv commentSubmission to SciPost

References in corpus (46)

• The density-matrix renormalization group in the age of matrix product states
• Spin Liquid Ground State of the $S=1/2$ Kagome Heisenberg Model
• The Kernel Polynomial Method
• Unifying time evolution and optimization with matrix product states
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• From density-matrix renormalization group to matrix product states
• Gapless spin-liquid ground state in the $S=1/2$ kagome antiferromagnet
• First excitations of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice
• Gapless spin-liquid phase in the kagome spin-1/2 Heisenberg antiferromagnet
• Finite Temperature Density Matrix Renormalization using an enlarged Hilbert space
• Signatures of Dirac cones in a DMRG study of the Kagome Heisenberg model
• Towards a fullerene-based quantum computer
• Generic Construction of Efficient Matrix Product Operators
• Gapped spin liquid with ${\mathbb{Z}}_2$-topological order for kagome Heisenberg model
• Magneto-thermodynamics of the spin-1/2 Kagome antiferromagnet
• Numerical-Diagonalization Study of Spin Gap Issue of the Kagome Lattice Heisenberg Antiferromagnet
• Superconductivity in a single C60 transistor
• The $S=1/2$ Kagome Heisenberg Antiferromagnet Revisited
• Magnetism of the N=42 kagome lattice antiferromagnet
• Deconfined criticality in the frustrated Heisenberg honeycomb antiferromagnet
• Triplet and Singlet Excitations in the Valence Bond Crystal Phase of Kagome Lattice Heisenberg Model
• Thermodynamics of quantum Heisenberg spin chains
• Magnetic Properties of Undoped $C_{60}$
• The Antiferromagnetic Heisenberg Model on Clusters with Icosahedral Symmetry
• Highly Frustrated Magnetic Clusters: The kagome on a sphere
• Properties of highly frustrated magnetic molecules studied by the finite-temperature Lanczos method
• Magnetic susceptibility and specific heat of the spin-1/2 Heisenberg model on the kagome lattice and experimental data on ZnCu3(OH)6Cl2
• Specific heat of the S=1/2 Heisenberg model on the kagome lattice: high-temperature series expansion analysis
• The pyrochlore S=1/2 Heisenberg antiferromagnet at finite temperature
• Thermodynamics of Spin-1/2 Kagomé Heisenberg Antiferromagnet: Algebraic Paramagnetic Liquid and Finite-Temperature Phase Diagram
• Enhancing superconductivity in A3C60 fullerides
• Quantum magnetism on the Cairo pentagonal lattice
• Magnetic Silicon Fullerene
• The $s=1/2$ Antiferromagnetic Heisenberg Model on Fullerene-Type Symmetry Clusters
• Correlation functions of the spin-1/2 anti-ferromagnetic Heisenberg chain: exact calculation via the generating function
• Large-scale numerical investigations of the antiferromagnetic Heisenberg icosidodecahedron
• Competing Spin Liquid Phases in the S=$\frac{1}{2}$ Heisenberg Model on the Kagome Lattice
• Interpolation between low and high temperatures of the specific heat for spin systems
• Strong Correlation Effects in the Fullerene C20
• Variational Hilbert space truncation approach to quantum Heisenberg antiferromagnets on frustrated clusters
• Correlations for the S=1/2 Antiferromagnet on a Truncated Tetrahedron
• Vanishing Wilson ratio as the hallmark of quantum spin-liquid models
• Generalized spin density wave state of the Hubbard model on the C12 and C60 clusters
• Electronic Pair-Binding and Hund's Rule Violations in Doped $C_{60}$
• Extended Hubbard model on a C${}_{20}$ molecule
• Ground state magnetic response of two coupled dodecahedra

Cited by in corpus (9)

• Thermodynamics of the spin-half square-kagome lattice antiferromagnet
• Magnetism of the $s=1/2$ $J_1$-$J_2$ square-kagome lattice antiferromagnet
• Magnetic properties of a capped kagome molecule with 60 quantum spins
• Ground states of Heisenberg spin clusters from a cluster-based projected Hartree-Fock approach
• $\mathbf{\Delta }$S${}^z$=2 quantum magnetization discontinuities proportional in number to the spin s in C${}_{60}$: Origin and the role of symmetry
• Noncoplanar and chiral spin states on the way towards Néel ordering in fullerene Heisenberg models
• Energy Scale Deformation on Regular Polyhedra
• Quantum dimer model on fullerenes: resonance, scarring and confinement
• Low-spin ground state of the giant single-molecule magnets {Mn${}_{70}$} and {Mn${}_{84}$}