The pyrochlore S=1/2 Heisenberg antiferromagnet at finite temperature

Abstract

Frustrated three dimensional quantum magnets are notoriously impervious to theoretical analysis. Here we use a combination of three computational methods to investigate the three dimensional pyrochlore $S=1/2$ quantum antiferromagnet, an archetypical frustrated magnet, at finite temperature, $T$: canonical typicality for a finite cluster of $2\times 2\times 2$ unit cells (i.e. $32$ sites), a finite-$T$ matrix product state method on a larger cluster with $48$ sites, and the numerical linked cluster expansion (NLCE) using clusters up to $25$ lattice sites, which include non-trivial hexagonal and octagonal loops. We focus on thermodynamic properties (energy, specific heat capacity, entropy, susceptibility, magnetisation) next to the static structure factor. We find a pronounced maximum in the specific heat at $T=0.57J$, which is stable across finite size clusters and converged in the series expansion. This is well-separated from a residual amount of spectral weight of $0.47k_B\ln 2$ per spin which has not been released even at $T\approx 0.25J$, the limit of convergence of our results. This is a large value compared to a number of highly frustrated models and materials, such as spin ice or the kagome $S=1/2$ Heisenberg antiferromagnet. We also find a non-monotonic dependence on $T$ of the magnetisation at low magnetic fields, reflecting the dominantly non-magnetic character of the low-energy spectral weight. A detailed comparison of our results to measurements for the $S=1$ material NaCaNi${}_2$F${}_7$ yields rough agreement of the functional form of the specific heat maximum, which in turn differs from the sharper maximum of the heat capacity of the spin ice material Dy${}_2$Ti${}_2$O${}_7$, all of which are yet qualitatively distinct from conventional, unfrustrated magnets.

arXiv comment23 pages, 15 figures

References in corpus (65)

• The density-matrix renormalization group in the age of matrix product states
• Efficient simulation of one-dimensional quantum many-body systems
• Magnetic Pyrochlore Oxides
• Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• The foundations of statistical mechanics from entanglement: Individual states vs. averages
• Time-dependent variational principle for quantum lattices
• Unifying time evolution and optimization with matrix product states
• Canonical Typicality
• Time-evolution methods for matrix-product states
• Computational Studies of Quantum Spin Systems
• Quantum Spin Ice: A Search for Gapless Quantum Spin Liquids in Pyrochlore Magnets
• Properties of a classical spin liquid: the Heisenberg pyrochlore antiferromagnet
• From density-matrix renormalization group to matrix product states
• Pyrochlore Antiferromagnet: A Three-Dimensional Quantum Spin Liquid
• Spin Ice, Fractionalization and Topological Order
• New Trends in Density Matrix Renormalization
• Finite Temperature Density Matrix Renormalization using an enlarged Hilbert space
• Absence of superconductivity in the pure two-dimensional Hubbard model
• Minimally Entangled Typical Thermal State Algorithms
• The Ergodic Side of the Many-Body Localization Transition
• Dipolar spin correlations in classical pyrochlore magnets
• Minimally entangled typical quantum states at finite temperature
• Canonical Thermal Pure Quantum State
• Thermal Pure Quantum States at Finite Temperature
• Frustrated quantum rare-earth pyrochlores
• Numerical Linked-Cluster Approach to Quantum Lattice Models
• A Strictly Single-Site DMRG Algorithm with Subspace Expansion
• Time evolution algorithms for Matrix Product States and DMRG
• Is the Yb2Ti2O7 pyrochlore a quantum spin ice?
• Singlet Excitations in Pyrochlore: A Study of Quantum Frustration
• A Short Introduction to Numerical Linked-Cluster Expansions
• Numerical Linked-Cluster Algorithms. I. Spin systems on square, triangular, and kagome lattices
• Thermodynamics of strongly interacting fermions in two-dimensional optical lattices
• Continuum of quantum fluctuations in a three-dimensional $S=1$ Heisenberg magnet
• Quantum and Classical Phases of the Pyrochlore Heisenberg Model with Competing Interactions
• Are multiphase competition & order-by-disorder the keys to understanding Yb2Ti2O7?
• Antiferromagnetic Quantum Spins on the Pyrochlore Lattice
• SU(2)-invariant spin-1/2 Hamiltonians with RVB and other valence bond phases
• Specific heat of the S=1/2 Heisenberg model on the kagome lattice: high-temperature series expansion analysis
• High-dimensional fractionalization and spinon deconfinement in pyrochlore antiferromagnets
• From Spin Glass to Quantum Spin Liquid Ground States in Molybdate Pyrochlores
• Numerical Linked-Cluster Algorithms. II. t-J models on the square lattice
• Spin-Ice State of the Quantum Heisenberg Antiferromagnet on the Pyrochlore Lattice
• Thermodynamic properties of the Yb2Ti2O7 pyrochlore as a function of temperature and magnetic field: validation of a quantum spin ice exchange Hamiltonian
• Signatures of a gearwheel quantum spin liquid in a spin-$\frac{1}{2}$ pyrochlore molybdate Heisenberg antiferromagnet
• Monopole Flux State on the Pyrochlore Lattice
• Quantum spin ice with frustrated transverse exchange: from pi-flux phase to nematic quantum spin liquid
• Instabilities of a U(1) quantum spin liquid in disordered non-Kramers pyrochlores
• Corrections to Pauling residual entropy and single tetrahedron based approximations for the pyrochlore lattice Ising antiferromagnet
• Order by disorder and gauge-like degeneracy in quantum pyrochlore antiferromagnet
• Large-scale numerical investigations of the antiferromagnetic Heisenberg icosidodecahedron
• Adapting Planck's route to investigate the thermodynamics of the spin-half pyrochlore Heisenberg antiferromagnet
• Quantum dimer models and effective Hamiltonians on the pyrochlore lattice
• Thermodynamics and phase transitions for the Heisenberg model on the pinwheel distorted kagome lattice
• Spin liquid and quantum phase transition without symmetry breaking in a frustrated three-dimensional Ising model
• Effect of particle statistics in strongly correlated two-dimensional Hubbard models
• Thermodynamics of the pyrochlore-lattice quantum Heisenberg antiferromagnet
• Thermodynamics of the Antiferromagnetic Heisenberg Model on the Checkerboard Lattice
• Theory of antiferromagnetic Heisenberg spins on breathing pyrochlore lattice
• Numerical study of the thermodynamics of clinoatacamite
• The spin-1/2 Heisenberg antiferromagnet on the pyrochlore lattice: An exact diagonalisation study
• Quantum generalized constant coupling model for geometrically frustrated antiferromagnets
• Anharmonic Ground state selection in the pyrochlore antiferromagnet
• Finite-size scaling of typicality-based estimates

Cited by in corpus (37)

• The case for a U(1)${}_{\pi }$ Quantum Spin Liquid Ground State in the Dipole-Octupole Pyrochlore Ce${}_2$Zr${}_2$O${}_7$
• Possible inversion symmetry breaking in the $S=1/2$ pyrochlore Heisenberg magnet
• Multiloop functional renormalization group approach to quantum spin systems
• Pseudo-fermion functional renormalization group for spin models
• Quantum effects on unconventional pinch point singularities
• Thermodynamics of the spin-half square-kagome lattice antiferromagnet
• Quantum Skyrmion Lattices in Heisenberg Ferromagnets
• The antiferromagnetic $S=1/2$ Heisenberg model on the ${\text{C}}_{60}$ fullerene geometry
• Dipolar spin ice regime proximate to an all-in-all-out Néel ground state in the dipolar-octupolar pyrochlore Ce${}_2$Sn${}_2$O${}_7$
• Projective symmetry group classification of chiral ${\mathbb{Z}}_2$ spin liquids on the pyrochlore lattice: application to the spin-$1/2$ XXZ Heisenberg model
• Quantum Spin Ice Response to a Magnetic Field in the Dipole-Octupole Pyrochlore Ce${}_2$Zr${}_2$O${}_7$
• Abundance of hard-hexagon crystals in the quantum pyrochlore antiferromagnet
• Quantum quench dynamics in the transverse-field Ising model: A numerical expansion in linked rectangular clusters
• Magnetism of the $s=1/2$ $J_1$-$J_2$ square-kagome lattice antiferromagnet
• Enhanced symmetry-breaking tendencies in the $S=1$ pyrochlore antiferromagnet
• $\mu$SR Study of the Dipole-Octupole Quantum Spin Ice Candidate Ce${}_2$Zr${}_2$O${}_7$
• Spin-half Heisenberg antiferromagnet on a symmetric sawtooth chain: Rotation-invariant Green's functions and high-temperature series
• Thermally enhanced Majorana-mediated spin transport in the Kitaev model
• Thermodynamics of the $S=1/2$ hyperkagome-lattice Heisenberg antiferromagnet
• Signatures of the finite-temperature mirror symmetry breaking in the $S$=1/2 Shastry-Sutherland model
• Finite-temperature phase transitions in $S=1/2$ three-dimensional Heisenberg magnets from high-temperature series expansions
• Linked Cluster Expansions via Hypergraph Decompositions
• Magnetic properties of a capped kagome molecule with 60 quantum spins
• Magnetization process and ordering of the $S=1/2$ pyrochlore magnet in a field
• Many-body localization and delocalization dynamics in the thermodynamic limit
• Two-Peak Heat Capacity Accounts for $R\ln (2)$ Entropy and Ground State Access in the Dipole-Octupole Pyrochlore Ce${}_2$Hf${}_2$O${}_7$
• Single Crystal Diffuse Neutron Scattering Study of the Dipole-Octupole Quantum Spin Ice Candidate Ce${}_2$Zr${}_2$O${}_7$: No Apparent Octupolar Correlations Above $T=0.05$ K
• Order, Disorder and Monopole Confinement in the Spin-$1/2$ XXZ Model on a Pyrochlore Tube
• L-based numerical linked cluster expansion for square lattice models
• DanceQ: High-performance library for number-conserving bases
• Spin and quadrupole correlations by three-spin interaction in the frustrated pyrochlore magnet Tb${}_{2+x}$Ti${}_{2-x}$O${}_{7+y}$
• Phase diagram of the antiferromagnetic $J_1$-$J_2$ spin-$1$ pyrochlore Heisenberg model
• Real-space spectral simulation of quantum spin models: Application to generalized Kitaev models
• Magnetostriction in the $J$-$K$-$\Gamma$ model: Application of the numerical linked cluster expansion
• Quantitative functional renormalization for three-dimensional quantum Heisenberg models
• Thermodynamics of the Heisenberg antiferromagnet on the maple-leaf lattice
• Three-dimensional unfrustrated and frustrated quantum Heisenberg magnets. Specific heat study