We present low-temperature static and dynamic properties of the quantum one-dimensional isotropic integer spin Heisenberg magnet with antiferromagnetic nearest-neighbour (nn) and next-nearest-neighbour (nnn) interactions. The modified spin-wave theory is used to provide quantities such as the spin-wave dispersion relation, the ground-state energy, the gap and its dependence with temperature, and the asymptotic behaviour of the spin–spin correlation function. The ground state energy and the singlet–triplet energy gap are obtained for several values of j, defined as the ratio of the nnn interaction constant to the nn one. Our results show that the ground-state and the gap energies increase with j, in accordance with numerical results available in the literature. The calculation of the dynamic correlation function is performed using the projection operator formalism: the procedure includes up to two-magnon processes. We show that, depending on the values of the frustration parameter j, the wavevector and the temperature, a double-peak structure for the dynamical correlation function can develop.
We have performed large-scale molecular dynamics simulations of a dynamical variant of the classical Heisenberg model in which the spins are replaced by interacting "linear molecules," each of which has two rotational degrees of freedom. The Hamiltonian consists of rotational kinetic-energy terms as well as nearest-neighbor Heisenberg-like interactions $\ensuremath{-}J{\mathrm{s}}_{i}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{s}}_{j}$, where
si is a unit vector specifying the orientation of the molecule at lattice site
i. Systems of size up to
643 spins on the simple cubic lattice have been studied, and thermostatting is used to maintain strictly constant temperature. We determined the dynamic structure function from the time- and space-displaced correlation functions, and found good agreement with the predictions of the dynamic scaling theory with a dynamic critical exponent of
z=1.5. Results are compared and contrasted with data from spin-dynamics calculations on classical Heisenberg ferromagnets and antiferromagnets.
The spin-1=2 Heisenberg model on the pyrochlore lattice is an iconic frustrated three-dimensional spin system with a rich phase diagram.Besides hosting several ordered phases, the model is debated to possess a spin-liquid ground state when only nearest-neighbor antiferromagnetic interactions are present.Here, we contest this hypothesis with an extensive numerical investigation using both exact diagonalization and complementary variational techniques.Specifically, we employ a resonating-valence-bond-like, manyvariable, Monte Carlo ansatz and convolutional neural network quantum states for (variational) calculations with up to 4 × 4 3 and 4 × 3 3 spins, respectively.We demonstrate that these techniques yield consistent results, allowing for reliable extrapolations to the thermodynamic limit.We consider the ðλ; j 2 =j 1 Þ parameter space, with j 2 , j 1 being nearest and next-to-nearest neighbor interactions and λ the XXZ interaction anisotropy.Our main results are (1) the determination of the phase transition between the putative spin-liquid phase and the neighboring magnetically ordered phase and (2) a careful characterization of the ground state in terms of symmetry-breaking tendencies.We find clear indications of a dimer order with spontaneously broken inversion and rotational symmetry, calling the scenario of a featureless quantum spin liquid into question.Our work showcases how many-variable variational techniques can be used to make progress in answering challenging questions about three-dimensional frustrated quantum magnets.
For quantum spin systems in equilibrium, the dynamic structure factor (DSF) is among the most feature-packed experimental observables. However, from a theory perspective it is often hard to simulate in an unbiased and accurate way, especially for frustrated and high-dimensional models at intermediate temperature. To address this challenge, we compute the DSF from a dynamic extension of the high-temperature expansion to frequency moments. We focus on nearest-neighbor Heisenberg models with spin lengths S=1/2 and 1. We provide comprehensive benchmarks and consider a variety of frustrated two- and three-dimensional antiferromagnets as applications. In particular we shed new light on the anomalous intermediate temperature regime of the S=1/2 triangular lattice model and reproduce the DSF measured recently for the S=1 pyrochlore material NaCaNi_{2}F_{7}. An open-source numerical implementation for arbitrary lattice geometries is also provided.
We use a combination of three computational methods to investigate the notoriously difficult frustrated three-dimensional pyrochlore
S=21 quantum antiferromagnet, at finite temperature
T: canonical typicality for a finite cluster of $2\ifmmode\times\else\texttimes\fi{}2\ifmmode\times\else\texttimes\fi{}2$ 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, including nontrivial hexagonal and octagonal loops. We calculate thermodynamic properties (energy, specific heat capacity, entropy, susceptibility, magnetization) and 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. At $T\ensuremath{\approx}0.25J$ (the limit of convergence of our method), the residual entropy per spin is
0.47kBln2, which is relatively large compared to other frustrated models at this temperature. We also observe a nonmonotonic dependence on
T of the magnetization at low magnetic fields, reflecting the dominantly nonmagnetic character of the low-energy states. A detailed comparison of our results to measurements for the
S=1 material
NaCaNi2F7 yields a 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
Dy2Ti2O7.
We present exact diagonalization calculations for the spin-1/2 nearest-neighbor antiferromagnet on the pyrochlore lattice. We study a section of the lattice in the [111] direction and analyze the Hamiltonian of the breathing pyrochlore system with two coupling constants
J1 and
J2 for tetrahedra of different orientations and investigate the evolution of the system from the limit of disconnected tetrahedra (
J2=0) to a correlated state at
J1=J2. We evaluate the low-energy spectrum, two and four spin correlations, and spin chirality correlations for a system size of up to 36 sites. The model shows a fast decay of spin correlations and we confirm the presence of several singlet excitations below the lowest magnetic excitation. We find chirality correlations near
J1=J2 to be small at the length scales available at this system size. Evaluation of dimer-dimer correlations and analysis of the nature of the entanglement of the tetrahedral unit shows that the triplet sector of the tetrahedron contributes significantly to the ground-state entanglement at
J1=J2.