Session X8: Focus Session: Frustrated Magnetism - Theory

Spin wave theory study of neutron intensity, magnetic field, and anisotropy of Type IIA FCC antiferromagnet

We study the spin dynamics in a 3D quantum antiferromagnet on a face-centered cubic (FCC) lattice. The effects of magnetic field, single-ion anisotropy, and biquadratic interactions are investigated using linear spin wave theory with Dyson-Maleev transformation for spins in a canted basis. We calculate the expected finite frequency neutron scattering intensity and give qualitative criteria for typical FCC materials MnO and CoO. The magnetization reduction due to quantum zero point fluctuations is also analyzed.   

Lifetime of gapped excitations in antiferromagnets

We show that local modulations of magnetic couplings may have a profound effect on the temperature-dependence of the relaxation rate of gapped excitations in a class of antiferromagnets in which gapless modes are also present. Considering a prototypical 2D XY antiferromagnet with random disorder we find that the disorder-induced relaxation rate of the gapped mode should greatly exceed the effect of conventional magnon-magnon scattering, which becomes negligible at low temperatures. Our results compare favorably with the available experimental data. Generalizations to the other systems are discussed.   

Effect of Interlayer Coupling on Field-Induced Magnon Decays in Square-Lattice Antiferromagnet

We study the high-field magnon dynamics in the quasi-2D tetragonal Heisenberg antiferromagnet. Within spin-wave theory, we show that non-zero interlayer coupling mitigates singular corrections to the excitation spectrum occurring above the threshold field that would otherwise require a self-consistent approach beyond the Born approximation. Increasing field yields widening two-magnon sidebands with significant shifting of the spectral weight away from the quasi-particle peak. We examine the dynamic structure factor with interlayer coupling corresponding to realistic materials.   

Detecting non-magnetic excitations in quantum magnets

Many unconventional quantum phases host special non-magnetic excitations such as photons and visons. We discuss two possible ways to detect these excitations experimentally. Firstly, spin-lattice coupling mixes the excitations with phonons. The phonon spectral function acquires new features that can be detected by neutron or X-ray scattering. Secondly, valence-bond fluctuations translate into charge density fluctuations on non-bipartite lattices. Such charge fluctuations can be characterized by conventional spectroscopies such as Terahertz spectroscopy. Observation of exotic singlet excitations would provide positive identification of unconventional quantum phases in frustrated antiferromagnets.   

Finite temperature phase diagram of quantum compass model

The quantum compass model has been proposed as a simplified model to study Mott insulators with orbital degeneracy and, more recently, as a candidate model to study protected non-local qubits. In this talk we will show that in addition to well known bond-directional ordering, there is additional ordering associated with long range string operators. We will discuss quantum Monte Carlo results that explore the thermodynamics of non-local order in the quantum compass model.   

Order by geometrical disorder in a 2D quantum antiferromagnet

We consider the effects of random fluctuations in the local geometry on the ground state properties of a two-dimensional quantum antiferromagnet. We analyse the behavior of spins described by the Heisenberg model as a function of what we call ``phason flip disorder,'' following a terminology used for aperiodic systems. The calculations were carried out both within linear spin wave theory and using quantum Monte Carlo simulations. An ``order by disorder'' phenomenon is observed in this model, wherein antiferromagnetism is found to be enhanced by phason disorder. The value of the staggered order parameter increases with the number of defects, accompanied by an increase in the ground state energy of the system. We furthermore find a long-ranged attractive Casimir-like force between two domain walls of defects separated by a finite distance.   

From Popov-Fedotov case to universal fermionization

We show that Popov-Fedotov trick of mapping spin-1/2 lattice systems on two-component fermions with imaginary chemical potential readily generalizes to bosons with a fixed (but not limited) maximal site occupation number, as well as to fermionic Hamiltonians with various constraints on the site Fock states. In a general case, the mapping---fermionization---is on multi-component fermions with many-body non-Hermitian interactions. Additionally, the fermionization approach allows one to convert large many-body couplings into single-particle energies, rendering the diagrammatic series free of large expansion parameters; the latter is essential for the efficiency and convergence of the diagrammatic Monte Carlo method.   

Universality of modulation length exponents

We study systems (classical or quantum) with general pairwise interactions. Our prime interest is in frustrated spin systems. First, we focus on systems with a crossover temperature $T^*$ across which the correlation function changes from exhibiting commensurate to incommensurate modulations. We report on a {\em new exponent}, $\nu_L$, characterizing the universal nature of this crossover. Near the crossover, the characteristic wave-vector $k$ on the incommensurate side differs from that on the commensurate side, $q$ by $|k-q|\propto|T-T^*|^{\nu_L}$. We find, in general, that $\nu_L=1/2$, or in some special cases, other rational numbers. We discuss applications to the axial next nearest neighbor Ising model, Fermi systems (with application to the metal to band insulator transition) and Bose systems. Second, we obtain a universal form of the high temperature correlation function in general systems. From this, we show the existence of a diverging correlation length in the presence of long range interactions. Such a correlation length tends to the screening length in the presence of screening. We also find a way of obtaining the pairwise interaction potentials in the high temperature phase from the correlation functions.   

Restricted Spin Set Lattice Models: A Route to Topological Order

A typical lattice gauge model configuration consists of elements of a finite symmetry group $G$ placed on directed edges of a two-dimensional lattice. We consider generalized models\footnote{C. L. Henley, J. Phys. Condens. Matter. 23, 164212 (2011).} which are defined by instead only allowing elements from a subset $S \subset G$ consisting of certain classes of group elements. The subset restriction can be regarded as a new (but discrete) tunable model parameter, providing a novel pathway to topologically ordered phases. Taking a small allowed set $S$, we can realize well understood critical models (e.g. the square lattice ice model or dimer covering); in contrast, for large enough $S$ the configuration ensemble realizes a form of topological order. Using a sequence of sets $S_1 \subset S_2 \subset \ldots$, we can ``interpolate'' from one kind of state to the other. This is confirmed by Monte Carlo simulations, measuring two characteristic properties: (1) the distribution of separations between two (possibly deconfined) topological defects, and (2) the relative probabilities of different sectors (sub-ensembles with inequivalent products of the group elements around the periodic boundary conditions). We also discuss how to construct quantum-mechanical extensions of these models.   

Stability of the quantum Lifshitz model in 2+1 Dimensions

Magnetic and electric perturbations to the quantum Lifshitz model in 2+1 dimensions are examined in this paper. The quantum Lifshitz model is an effective field theory for quantum critical systems that include generalized 2D quantum dimer models in bipartite lattices. Magnetic perturbations break the dimer conservation law. Electric excitations have been studied extensively both in the classical 3D model and in the quantum 2D model, but magnetic vortex excitations have been ignored. While they are forbidden in classical 3D statistical mechanics, they are allowed in the quantum version. To study the interplay of both excitations, we perform a perturbative renormalization group study to one loop order. This is done by generalizing the operator product expansion to anisotropic models. The relation with recent classical Monte Carlo simulations will be discussed.   

Supersymmetry in strongly correlated fermion models

We investigate the Fendley and Schoutens~\footnote{ P. Fendley and K. Schoutens, Phys. Rev. Lett. 90, 120402 (2003).} model of hard core fermions on a lattice which have hopping elements $t$, and potential terms $V$ which include a second-neighbor repulsion with some multi-particle terms. At the special point $t=V$, the Hamiltonian is $H = \{Q^\dagger(r), Q\}$ with $Q = \sum_r q(r)= \sum_r c(r)P(r)$, where $c(r)$ is an annihilation operator and $P(r)$ enforces the hard core. That means the system acquires an exact non-relativistic supersymmetry, and for a range of fillings has a large number of zero-energy ground states~$^1$. To better understand the nature of the zero-energy states and excitations, we perform exact diagonalizations on finite clusters for the square and triangular lattice, different fillings and center of mass momenta. In momentum sectors with unique zero energy ground states we find a menagerie of symmetry breaking patterns in the density-density correlation functions and we investigate them further by evaluating the entanglement spectrum. In momentum sectors with degenerate ground states we search for topological ground states using using the numerical Berry matrix method~\footnote{ E. Kapit, P. Ginsparg, and E. Mueller, arXiv:1109.4561}.   

First-principles study on electronic properties of the pyrochlore oxide Cd2Os2O7

The pyrochlore oxide Cd2Os2O7 is one of 5d pyrochlore oxides in which the interplay of geometrical frustration, electron correlation, and spin-orbit coupling is expected. This compound exhibits a metal-insulator transition at 227 K, below which the emergence of a magnetic order has been suggested by experiments. Despite extensive studies for over thirty years, however, the nature of the low-temperature phase remains to be clarified. We depict the ground-state phase diagram based on the LSDA+$U$ method (LSDA denotes local spin density approximation). We find that the all-in/all-out non-collinear magnetic order is stable in a wide range of $U$. We show that the easy-axis anisotropy arising from the spin-orbit coupling plays a significant role in stabilizing the all-in/all-out magnetic order. A pseudo gap extending up to high energy is found to appear near a continuous metal-insulator transition between an antiferromagnetic metallic phase and an antiferromagnetic insulating phase. Based on the computed results, we discuss possible origins of peculiar low-temperature properties observed in experiments.   

Exchange and Magnetic Anisotropic Interactions of Magnetic Ions in Antiferromagnetic Materials

Investigations of exchange and magnetic anisotropic interactions, based on materials crystallographic and magnetic symmetry, introducing quadratic forms of thermodynamic potentials, invarianted with respect to operations of magnetic symmetry groups and presented in irreducible representations of interacting ions magnetic moments, are in discussions in connection with considerations of symmetric, Anderson exchange interactions, based on Hubbard Hamiltonians, that indicates dependencies of symmetric exchange on electrons transferrings between magnetic, nonmagnetic ions, electrons kinetic energy, Coulomb interactions and, determined by crystal fields, energy levels. As example, according to symmetry for some rhombohedral structures, spin Hamiltonians of symmetric, Anderson and antisymmetric, Dzyaloshinskii-Moria exchange, H$_{ex}=\sum _{ij}$J$_{ij}$(\textbf{S}$_{i}$\textbf{S}$_{j})-\sum _{ij}$D$_{ij,z}$(\textbf{S}$_{ix}$\textbf{S}$_{jy}-$\textbf{S}$_{iy}$\textbf{S}$_{jx})$, with D$_{ij,z}$ in abs values. Magnetic field dependencies of separate, three components of samples magnetic moments of vector v.s.magnetometer, indicating magnetic moments orientations, present direct information about interactions of magnetic ions, especially with high spin orbit interactions.