Magnetic field induced multiple non-Dirac nodal-lines are found to emerge in the triplet dispersion bands of a frustrated spin-1/2 antiferromagnetic model on the CaVO lattice. Plaquette and bond operator formalisms have been employed to obtain the triplet plaquette and bond excitations for two different parameter regimes in the presence of nearest and next-nearest-neighbor Heisenberg interactions based on the plaquette-resonating-valence-bond and dimerized ground states, respectively. In the absence of magnetic field a pair of six-fold degenerate nodal-loops with distinct topological feature is noted in the plaquette excitations. They are found to split into three pairs of two-fold degenerate nodal-loops in the presence of magnetic field. In the other parameter regime, system hosts two-fold degenerate multiple nodal-lines with a variety of shapes in the triplon dispersion bands in the presence of magnetic field. Ground state energy and spin gap have been determined additionally for the two regimes. Those nodal-lines are expected to be detectable in neutron scattering experiment on the frustrated antiferromagnet, CaV$_4$O$_9$.
We investigate the physics of frustrated 3-leg Hubbard ladders in the band limit, when hopping across the ladder's rungs (t$_{\perp}$) is of the same order as hopping along them (t) much greater than the onsite Coulomb repulsion (U). We show that this model exhibits a striking electron-hole asymmetry close to half-filling: the hole-doped system at low temperatures develops a Resonating Valence Bond (RVB)-like d-wave gap (pseudogap close to ($π$,0)) coinciding with gapless nodal excitations (nodal liquid); in contrast, the electron-doped system is seen to develop a Mott gap at the nodes, whilst…
The experimental observation of a spin-gap in the antiferromagnetic spin-1/2 compound $CaV_4O_9$ has been attributed to the formation of a plaquette resonating-valence-bond (PRVB) state in the underlying 1/5-depleted square lattice. We construct a spin-1/2 model on the 1/5-depleted lattice for which the PRVB state can be shown to be the exact ground state in a particular parameter regime. In a subspace of this parameter regime, the first excited state can be calculated exactly. In a different parameter regime, the dimer state is shown to be the exact ground state.
We demonstrate the appearance of symmetry protected triplon Dirac modal lines in the low energy excitation spectrum of a realistic microscopic model of the geometrically frustrated quantum magnet SrCu2(BO3)2 in its high symmetry phase. The symmetry-allowed Dzyaloshinskii-Moriya interactions induce dispersive trilpon bands within the bond-operator formalism that cross linearly over an extended closed path in the Brillouin zone. Our results establish that the nodal lines are protected by a $U(1)$-symmetry and robust against perturbations that preserve this symmetry. In the presence of a longitud…
The formation of coplanar spin spirals is a common motif in the magnetic ordering of many frustrated magnets. For classical antiferromagnets, geometric frustration can lead to a massively degenerate ground state manifold of spirals whose propagation vectors can be described, depending on the lattice geometry, by points (triangular), lines (fcc), surfaces (frustrated diamond) or completely flat bands (pyrochlore). Here we demonstrate an exact mathematical correspondence of these spiral manifolds of classical antiferromagnets with the Fermi surfaces of free-fermion band structures. We provide an…
Fermionic valence bond approach in terms of SU(4) representation is proposed to describe the $J_{1}-J_{2}$ frustrated Heisenberg antiferromagnetic (AF) model on a {\it bipartite} square lattice. A uniform mean field solution without breaking the translational and rotational symmetries describes a valence bond spin liquid state, interpolating the two different AF ordered states in the large $J_{1}$ and large $J_{2}$ limits, respectively. This novel spin liquid state is gapless with the vanishing density of states at the Fermi nodal points. Moreover, a sharp resonance peak in the dynamic structu…
We study the nontrivial linear magnon band crossings in the collinear antiferromagnets on the two-dimensional (2D) CaVO lattice, also realized in some iron-based superconductors such as AFe$_{1.6+x}$Se$_2$ (A = K, Rb, Cs). It is shown that the combination of space-inversion and time-reversal symmetry ($\mathcal{PT}$-symmetry) leads to doubly-degenerate eight magnon branches, which cross each other linearly along a one-dimensional loop in the 2D Brillouin zone. We show that the Dirac nodal loops (DNLs) are not present in the collinear ferromagnet on this lattice. Thus, the current 2D antiferrom…
Ultracold atoms loaded on optical lattices can provide unprecedented experimental systems for the quantum simulations and manipulations of many quantum phases and quantum phase transitions between these phases. However, so far, how to detect these quantum phases and phase transitions effectively remains an outstanding challenge. In this paper, we will develop a systematic and unified theory of using the optical Bragg scattering, atomic Bragg scattering or cavity QED to detect the ground state and the excitation spectrum of many quantum phases of interacting bosons loaded in bipartite and frust…
CaV$_2$O$_4$ is a spin-1 antiferromagnet, where the magnetic vanadium ions are arranged on quasi-one-dimensional (1D) zig-zag chains with potentially frustrated antiferromagnetic exchange interactions. High temperature susceptibility and single-crystal neutron diffraction measurements are used to deduce the non-collinear magnetic structure, dominant exchange interactions and orbital configurations. The results suggest that at high temperatures CaV$_2$O$_4$ behaves as a Haldane chain, but at low temperatures, orbital ordering lifts the frustration and it becomes a spin-1 ladder.
We construct and analyze a two-dimensional frustrated quantum spin model with plaquette order, in which the low-energy dynamics is controlled by spin singlets. At a critical value of frustration the singlet spectrum becomes gapless, indicating a quantum transition to a phase with dimer order. This T=0 transition belongs to the 3D Ising universality class, while at finite temperature a 2D Ising critical line separates the plaquette and dimerized phases. The magnetic susceptibility has an activated form throughout the phase diagram, whereas the specific heat exhibits a rich structure and a power…
Frustrated magnetic systems exhibit many fascinating phases. Prime among them are quantum spin liquids, where the magnetic moments do not order even at zero temperature. A subclass of quantum spin liquids called Kitaev spin liquids are particularly interesting, because they are exactly solvable, can be realized in certain materials, and show a large variety of gapless and gapped phases. Here, we show that non-symmorphic symmetries can enrich spin liquid phases, such that the low-energy spinon degrees of freedom form three-dimensional Dirac cones or nodal chains. In addition, we suggest how suc…
We present magnetic susceptibility measurements on MgV$_2$O$_5$, a compound in which the vanadium oxide planes have the same topology as in CaV$_2$O$_5$. The most striking property is that there is an energy gap of about 15 K, much smaller than in CaV$_2$O$_5$, where the values reported are of the order of 500 K. We show that this may be understood naturally in terms of the phase diagram of the frustrated, coupled ladder system. This analysis leads to the prediction that MgV$_2$O$_5$ should have incommensurate dynamic spin fluctuations.
The mixed spin-(1,1/2) Ising-Heisenberg double sawtooth ladder containing mixture of both spin-1 and spin-1/2 nodal atoms, and the spin-1/2 interstitial dimers is approximately solved by the transfer-matrix method. Here, we study in detail the ground-state phase diagrams, also influences of the bilinear exchange coupling on the rungs and cyclic four-spin exchange interaction in square plaquette of each block on the magnetization and magnetic susceptibility of the suggested ladder at low temperature. Such a double sawtooth ladder may be found in a Shastry-Sutherland Lattice-type. In spite of od…
The crystal and magnetic structures and underlying magnetic interactions of Bi4Fe5O13F, a model system for studying the physics of the Cairo pentagonal spin lattice, are investigated by transmission electron microscopy, low-temperature synchrotron x-ray and neutron powder diffraction, thermodynamic measurements, and density functional band-structure calculations. The crystal structure of Bi4Fe5O13F contains infinite rutile-like chains of edge-sharing FeO6 octahedra interconnected by the Fe2O7 groups of two corner-sharing FeO4 tetrahedra. The cavities between the chains are filled with the fluo…
Weyl nodes have been experimentally realized in photonic, electronic, and phononic crystals. However, magnonic Weyl nodes are yet to be seen experimentally. In this paper, we propose Weyl magnon nodes in noncoplanar stacked frustrated kagome antiferromagnets, naturally available in various real materials. Most crucially, the Weyl nodes in the current system occur at the lowest excitation and possess a topological (anomalous) thermal Hall effect, therefore they are experimentally accessible at low temperatures due to the population effect of bosonic quasiparticles. In stark contrast to other ma…
Pursuing fractionalized particles that do not bear properties of conventional measurable objects, exemplified by bare particles in the vacuum such as electrons and elementary excitations such as magnons, is a challenge in physics. Here we show that a machine-learning method for quantum many-body systems that has achieved state-of-the-art accuracy reveals the existence of a quantum spin liquid (QSL) phase in the region $0.49\lesssim J_2/J_1\lesssim0.54$ convincingly in spin-1/2 frustrated Heisenberg model with the nearest and next-nearest neighbor exchanges, $J_1$ and $J_2$, respectively, on th…
We study the propagation of photons in a one-dimensional environment consisting of two non-interacting species of photons frustratingly coupled to a single spin-1/2. The ultrastrong frustrated coupling leads to an extreme mixing of the light and matter degrees of freedom, resulting in the disintegration of the spin and a breakdown of the "dressed-spin", or polaron, description. Using a combination of numerical and analytical methods, we show that the elastic response becomes increasingly weak at the effective spin frequency, showing instead an increasingly strong and broadband response at high…
We propose a new form of the frustrated Heisenberg antiferromagnetic Hamiltonian with spatially anisotropic exchange parameters Jc, Ja, and Jac extended along the c, a, and a +/- c lattice directions and apply it to describe fascinating physics of copper carbodiimide CuNCN in the assumption of resonating valence bond (RVB) type of its phases. These are invoked to explain the intriguing absence of magnetic order in CuNCN down to 4 K. We show that the quasiparticle spectrum of the RVB model of the proposed Hamiltonian has three principal regimes: (i) one with two pairs of lines of nodes, (ii) on…
