Eighth-order high-temperature expansion for general Heisenberg Hamiltonians

Abstract

We explicitly calculate the moments $t_n$ of general Heisenberg Hamiltonians up to eighth order. They have the form of finite sums of products of two factors. The first factor is represented by a (multi-)graph which has to be evaluated for each particular system under consideration. The second factors are well-known universal polynomials in the variable $s(s+1)$, where $s$ denotes the individual spin quantum number. From these moments we determine the corresponding coefficients of the high-temperature expansion of the free energy and the zero field susceptibility by a new method. These coefficients can be written in a form which makes explicit their extensive character. Our results represent a general tool to calculate eighth-order high-temperature series for arbitrary Heisenberg models. The results are applied to concrete systems, namely to magnetic molecules with the geometry of the icosidodecahedron, to frustrated square lattices, and to the pyrochlore magnets. By comparison with other methods that have been recently applied to these systems, we find that the typical susceptibility maximum of the spin-$s$ Heisenberg antiferromagnet is well described by the eighth-order high-temperature series.

arXiv comment8 figures, 3 appendices

References in corpus (45)

• The density-matrix renormalization group in the age of matrix product states
• The density-matrix renormalization group
• Spin Ice State in Frustrated Magnetic Pyrochlore Materials
• Magnetic Monopoles in Spin Ice
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Thermodynamics of Spin S = 1/2 Antiferromagnetic Uniform and Alternating-Exchange Heisenberg Chains
• Effects of frustration on magnetic molecules: a survey from Olivier Kahn till today
• Ground-state phases of the spin-1/2 J_1-J_2 Heisenberg antiferromagnet on the square lattice: A high-order coupled cluster treatment
• The spin-1/2 J1-J2 Heisenberg antiferromagnet on the square lattice: Exact diagonalization for N=40 spins
• Many-body Green's function theory of Heisenberg films
• J_1-J_2 frustrated two-dimensional Heisenberg model: Random phase approximation and functional renormalization group
• Asymptotic scaling of the square lattice quantum Heisenberg antiferromagnet
• The J1-J2 model: First order phase transition versus deconfinement of spinons
• Finite temperature properties and frustrated ferromagnetism in a square lattice Heisenberg model
• Independent magnon states on magnetic polytopes
• Enhanced magnetocaloric effect in frustrated magnetic molecules with icosahedral symmetry
• Extension of the spin-1/2 frustrated square lattice model: the case of layered vanadium phosphates
• Highly Frustrated Magnetic Clusters: The kagome on a sphere
• Frustrated trimer chain model and Cu3Cl6(H2O)2 2H8C4SO2 in a magnetic field
• Properties of highly frustrated magnetic molecules studied by the finite-temperature Lanczos method
• Magnetic susceptibility of diluted pyrochlore and SCGO antiferromagnets
• Quantum rotational band model for the Heisenberg molecular magnet Mo72Fe30
• The frustrated spin-1/2 J1-J2 Heisenberg ferromagnet on the square lattice: Exact diagonalization and Coupled-Cluster study
• Frustration effects in magnetic molecules
• Phase Diagram of the BCC S=1/2 Heisenberg Antiferromagnet with First and Second Neighbor Exchange
• The Two-Dimensional S=1 Quantum Heisenberg Antiferromagnet at Finite Temperatures
• Saturation field of frustrated chain cuprates: broad regions of predominant interchain coupling
• Takahashi Integral Equation and High-Temperature Expansion of the Heisenberg Chain
• Thermodynamic properties of ferromagnetic mixed-spin chain systems
• Frustrated square lattice with spatial anisotropy: crystal structure and magnetic properties of PbZnVO(PO4)2
• Multiple nearest-neighbor exchange model for the frustrated magnetic molecules Mo72Fe30 and Mo72Cr30
• Influence of an inter-chain coupling on spiral ground-state correlations in frustrated spin-1/2 J1-J2 Heisenberg chains
• Determination of the exchange energies in Li2VOSiO4 from a high-temperature series analysis of the square lattice J1-J2 Heisenberg model
• Thermodynamics of a two-dimensional frustrated spin-1/2 Heisenberg ferromagnet
• High Temperature Expansion for Frustrated and Unfrustrated S=1/2 Spin Chains
• Curie and Neel Temperatures of Quantum Magnets
• Heisenberg exchange parameters of molecular magnets from the high-temperature susceptibility expansion
• E-band excitations in the magnetic Keplerate molecule Fe30
• Green's function theory of quasi-two-dimensional spin-half Heisenberg ferromagnets: stacked square versus stacked kagomé lattice
• The incarnation of the Nersesyan-Tsvelik model in (NO)[Cu(NO3)3]
• Sampling the two-dimensional density of states g(E,M) of a giant magnetic molecule using the Wang-Landau method
• Antiferromagnetic spin-1/2 chains in (NO)Cu(NO3)3: a microscopic study
• Classical generalized constant coupling model for geometrically frustrated antiferromagnets
• Field dependent thermodynamics and Quantum Critical Phenomena in the dimerized spin system Cu2(C5H12N2)2Cl4
• Strong-coupling Expansions at Finite Temperatures: Application to Quantum Disordered and Quantum Critical Phases

Cited by in corpus (48)

• Magnetism of the N=42 kagome lattice antiferromagnet
• First-principles determination of Heisenberg Hamiltonian parameters for the spin-1/2 kagome antiferromagnet ZnCu3(OH)6Cl2
• Frustrated two dimensional quantum magnets
• Tenth-order high-temperature expansion for the susceptibility and the specific heat of spin-s Heisenberg models with arbitrary exchange patterns: Application to pyrochlore and kagome magnets
• Spin-Ice State of the Quantum Heisenberg Antiferromagnet on the Pyrochlore Lattice
• Thermodynamic properties of highly frustrated quantum spin ladders: influence of many-particle bound states
• Magnetic excitations and electronic interactions in Sr${}_2$CuTeO${}_6$: a spin-1/2 square lattice Heisenberg antiferromagnet
• Commensurate and incommensurate magnetic order in spin-1 chains stacked on the triangular lattice in Li${}_2$NiW${}_2$O${}_8$
• Thermodynamics of anisotropic triangular magnets with ferro- and antiferromagnetic exchange
• Magnetic interactions in disordered perovskite PbFe_{1/2}Nb_{1/2}O_3 and related compounds. Dominance of nearest-neighbor interaction
• Adapting Planck's route to investigate the thermodynamics of the spin-half pyrochlore Heisenberg antiferromagnet
• Thermodynamics of the spin-half square-kagome lattice antiferromagnet
• Advanced Finite-Temperature Lanczos Method for anisotropic spin systems
• Ca2Y2Cu5O10: the first frustrated quasi-1D ferromagnet close to criticality
• Interpolation between low and high temperatures of the specific heat for spin systems
• Thermodynamics of the pyrochlore-lattice quantum Heisenberg antiferromagnet
• The planar triangular $S=3/2$ magnet AgCrSe${}_2$: magnetic frustration, short range correlations, and field tuned anisotropic cycloidal magnetic order
• Thermodynamics of delta-chain with ferro- and antiferromagnetic interactions
• Decorated Shastry-Sutherland lattice in the spin-1/2 magnet CdCu2(BO3)2
• Collinear order in a frustrated three-dimensional spin-$\frac{1}{2}$ antiferromagnet Li${}_2$CuW${}_2$O${}_8$
• Thermodynamics of the two-dimensional frustrated J1-J2 Heisenberg ferromagnet in the collinear stripe regime: Susceptibility and correlation length
• High-temperature expansion for frustrated magnets: Application to the J1-J2 model on the BCC lattice
• Thermodynamics of the frustrated $J_1$-$J_2$ Heisenberg ferromagnet on the body-centered cubic lattice with arbitrary spin
• Magnetism of the $s=1/2$ $J_1$-$J_2$ square-kagome lattice antiferromagnet
• Thermodynamics of the kagome-lattice Heisenberg antiferromagnet with arbitrary spin $S$
• Thermodynamics of the pyrochlore Heisenberg ferromagnet with arbitrary spin $S$
• Geometrical origin of ferrimagnetism and superparamagnetism in Fe-based double perovskite multiferroics
• Thermodynamic observables of Mn12-acetate calculated for the full spin-Hamiltonian
• Highly dispersive magnons with spin-gap like features in the frustrated ferromagnetic S=1/2 chain compound Ca2Y2Cu5O10 detected by inelastic neutron scattering
• $J_1$-$J_2$ square lattice antiferromagnetism in the orbitally quenched insulator MoOPO${}_4$
• Quantum magnetism in the frustrated square lattice oxyhalides YbBi2IO4 and YbBi2ClO4
• Spin-half Heisenberg antiferromagnet on a symmetric sawtooth chain: Rotation-invariant Green's functions and high-temperature series
• Static and dynamic magnetic properties of the spin-5/2 triangle lattice antiferromagnet Na3Fe(PO4)2 studied by 31P NMR
• Lieb-Mattis ferrimagnetism in diluted magnetic semiconductors
• Comment on `Oxygen vacancy-induced magnetic moment in edge-sharing CuO${}_2$ chains of Li${}_2$CuO${}_2$'
• High temperature series expansions of S = 1/2 Heisenberg spin models: algorithm to include the magnetic field with optimized complexity
• Thermodynamics of the $S=1/2$ hyperkagome-lattice Heisenberg antiferromagnet
• Degenerate ground state in the classical pyrochlore antiferromagnet Na${}_3$Mn(CO${}_3$)${}_2$Cl
• A case study of bilayered spin-$1/2$ square lattice compound [VO(HCOO)${}_2\cdot$(H${}_2$O)]
• Magnetic susceptibility of frustrated spin-s J1-J2 quantum Heisenberg magnets: High-temperature expansion and exact diagonalization data
• The spin-$\frac{1}{2}$ Heisenberg ferromagnet on the pyrochlore lattice: A Green's function study
• The general spin triangle
• Thermodynamics of the classical spin triangle
• Improving Variational Counterdiabatic Driving with Weighted Actions and Computer Algebra
• Thermal DMRG for highly frustrated quantum spin chains: a user perspective
• Universal fluctuating regime in triangular chromate antiferromagnets
• The classical spin triangle as an integrable system
• Origin of the intermediate-temperature magnetic specific heat capacity in the spin-liquid candidate Ca${}_{10}$Cr${}_7$O${}_{28}$