Bulletin of the American Physical Society
2005 APS March Meeting
Monday–Friday, March 21–25, 2005; Los Angeles, CA
Session S9: Geometrically Frustrated Magnets II |
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Sponsoring Units: GMAG Chair: Oleg Tchernyshov, Johns Hopkins University Room: LACC 153A |
Wednesday, March 23, 2005 2:30PM - 2:42PM |
S9.00001: Phase diagram of the S=1/2 checkerboard antiferromagnet Akira Furusaki, Leon Balents, Oleg Starykh We report the phase diagram of the S=1/2 Heisenberg antiferromagnet on the checkerboard lattice, also known as the crossed-chains lattice. It is assumed that the exchange coupling along the crossing chains, $J_2$, is different from that on the inter-chain (square-lattice) links, $J_1$. We show that in the one-dimensional limit $J_2 \gg J_1$, the ground state is spontaneously dimerized in the crossed-dimer pattern. At the isotropic planar pyrochlore point $J_2=J_1$, the ground state is also a valence-bond solid (VBS) but of the plaquette type, as is known from previous studies. We argue that these two VBS states may be connected, as a function of the ratio $J_2/J_1$, by an intermediate magnetically-ordered phase. Two quantum critical points, separating the ordered phase from dimerized VBS ones, are analyzed and argued to belong to the $O(3)$ universality class. [Preview Abstract] |
Wednesday, March 23, 2005 2:42PM - 2:54PM |
S9.00002: A soluble model for a Spin-1 Kagom\'{e} Antiferromagnet Kirill Shtengel, Gil Refael We propose an exactly soluble spin-1 model on a $2D$ Kagom\'{e} lattice. The Klein-type Hamiltonian involves interactions between nearest and next-nearest spins and, unlike the closely related AKLT Hamiltonians, has extensively degenerate ground states. These ground sates are characterised by an exponential fall-off of correlations between spins which strongly suggests a gap to the excited states. Simple spin-1 and spin-0 excitations can be viewed as bound states of $S=1/2$ spinons. We also show that generic Heisenberg-like perturbations lead to a unique ground state -- a featureless fluctuating valence bond ``solid'' obtained by placing a benzol ring on every hexagon of the lattice. Finally, we consider an additional term of the type $\alpha ({S^z})^2$ which can drive the system into another featureless ground state. We introduce the notion of ``wedge'' excitations that allow to distinguish between these states leading to the conclusion that these sates must be separated by at least one quantum phase transition. [Preview Abstract] |
Wednesday, March 23, 2005 2:54PM - 3:06PM |
S9.00003: Spectral analysis of higher spins (S$>$1/2) kagome systems Dommange Stephane, Laeuchli Andreas Martin, Mila Frederic, Fouet Jean Baptiste, Normand Bruce We will present some recent numerical results concerning higher spin kagome systems, with emphasis on S=3/2. We focus on pure systems calculating exact spectra for different cluster sizes and conclude that no magnetic long range order is found. We complete the analysis by describing some features of such systems doped with non-magnetic impurities. [Preview Abstract] |
Wednesday, March 23, 2005 3:06PM - 3:18PM |
S9.00004: Role of Quantum Fluctuations in the triangular antiferromagnet Cs$_2$CuCl$_4$ Martin Y. Veillette, John Chalker We have performed a detailed comparison of static properties of the anisotropic triangular antiferromagnet Cs$_2$CuCl$_4$ with a calculation taking into account the leading order of the zero point fluctuations at zero temperature. The Hamiltonian of the Cs$_2$CuCl$_4$ compound is known to a high degree of accuracy and allows for a parameter-free calculation. A distinction must be made between transverse and longitudinal field due to a weak Dzyaloshinkii-Moriya interaction that introduce an easy-plane anisotropy in the Hamiltonian. The phase diagram is determined in a classical approximation along the two field directions. Building on these results, we calculate the contribution of quantized spin-waves in a large S expansion to themagnetization, ordering wavevector, sublattice magnetization and transverse spin component. The results are shown to depend sensitively on the weak anisotropy. In high field, we find the zero-point fluctuations to be quenched and use a mapping to a dilute Bose gas to determine the exact quantum contribution near the critical field. The results of the linear spin wave analysis are found to be in excellent agreement with the experimental data. [Preview Abstract] |
Wednesday, March 23, 2005 3:18PM - 3:30PM |
S9.00005: Spin Structure Factor of the Frustrated Quantum Magnet $Cs_2 Cu Cl_4$. Denis Dalidovich, Rastko Sknepnek, Junhua Zhang, Catherine Kallin, John Berlinsky We present the results of a calculation of the spin structure factor for the two-dimensional antiferromagnet on the triangular lattice, with strong directional anisotropy in the nearest-neighbour exchange couplings. The corresponding Heisenberg Hamiltonian describes the physics following from neutron scattering measurements in the frustrated quantum magnet $Cs_2 Cu Cl_4$, [R. Coldea, et. al., Phys. Rev. B, {\bf 68}, 134424, (2003)]. Since the experimental data reveal the presence of a small but finite on-site magnetic moment $S_z$, the calculations are performed using the Holstein-Primakoff representation for spins. The results for the structure factor, computed up to the order in $1/S$ that takes into account interactions between magnons, are compared with experiment. [Preview Abstract] |
Wednesday, March 23, 2005 3:30PM - 3:42PM |
S9.00006: Superfluid-insulator transition in two-dimensional superfluids on the triangular lattice Anton Burkov, Leon Balents We report on a study of superfluid to Mott insulator transition in two-dimensional superfluids on the triangular lattice at rational fillings, with a particular emphasis on 1/2 and 1/3 fillings. This is a continuation of our earlier study (cond-mat/0408329) of superfluids on the square lattice. At 1/3 filling, not unexpectedly, we find a picture of the transition that is very similar to the 1/2 filling square lattice case. On the other hand, at 1/2 filling on the triangular lattice strong geometric frustration leads to a very different picture, with features that have no analogs in square lattice superfluids. We find that the low-energy action, describing the transition in this case, has an emergent nonabelian symmetry, not present at the microscopic level, and explore the physical consequences of this symmetry. We also identify the essential features of the insulating phases at 1/2 filling, in particular the prevalence of valence bond solid (VBS) phases over simple site-centered charge density wave phases. This has important implications for the search of microscopic models where VBS phases may be realized. [Preview Abstract] |
Wednesday, March 23, 2005 3:42PM - 3:54PM |
S9.00007: Topological degeneracy in the RVB phase of the Quantum Dimer Model on the triangular lattice Arnaud Ralko, Michel Ferrero, Federico Becca, Dimitri Ivanov, Frederic Mila Using numerical methods such as exact diagonalizations and Green function monte carlo (GFMC), we study ground state properties of the different topological sectors of the Quantum dimer model on the triangular lattice to characterize the phases of the system and the transition points between them. Thanks to the large sizes available with GFMC, we show in particular that in the thermodynamic limit, the four topological sectors are indeed degenerate. Finally, we show that the correlation functions are consistent with the identification of the ordered phases by Moessner and Sondhi. [Preview Abstract] |
Wednesday, March 23, 2005 3:54PM - 4:06PM |
S9.00008: Two Step Restoration of SU(2) Symmetry in a Frustrated Quantum Magnet Andreas L\"auchli, J.C. Domenge, C. Lhuillier, P. Sindzingre, M. Troyer We demonstrate the existence of a spin-nematic, moment-free phase in a quantum four-spin ring exchange model on the square lattice. This unusual quantum state is created by the interplay of frustration and quantum fluctuations which lead to a partial restoration of $SU(2)$ symmetry when going from a four- sublattice orthogonal biaxial N\'eel order to this exotic uniaxial magnet. A further increase of frustration drives a transition to a fully gapped $SU(2)$ symmetric valence bond crystal. [Preview Abstract] |
Wednesday, March 23, 2005 4:06PM - 4:18PM |
S9.00009: Spin charge sepration in the doped frustrated J1-J2-J3 Heisenberg antiferromagnet on the square lattice Matthieu Mambrini, Andreas Laeuchli, Didier Poilblanc We study undoped and doped frustrated J1-J2-J3 Heisenberg antiferromagnet on the square lattice using both exact diagonalization techniques and projections onto the short-range RVB subspace. The insulating system shows, in the vicinity of the $(J_3+J_2)/J_1 =0.5$ line, a magnetically disordered ground very well captured by a RVB wave function. The nature, dimer liquid or valence bond crystal, of such a RVB phase is characterized from the computation of dimer-dimer correlations and a singlet spectrum analysis of finite clusters up to 50 sites. We also show that a substancial reduction of the quasi-particle spectral weight of a doped hole can be related to the spin liquid character of the magnetic background. This suggests that spin-charge separation occurs in such a frustrated system. [Preview Abstract] |
Wednesday, March 23, 2005 4:18PM - 4:30PM |
S9.00010: Order in the resonating singlet valence plaquette model in three dimensions. Sergey Pankov, Roderich Moessner, Shivaji Sondhi We study a generalization of resonating valence bond (RVB) physics to three dimensions. In two dimensions short-range RVB models can exhibit fundamentally interesting phenomena like quantum liquid states with topological order and fractionalization. Whereas in the RVB case, the basic degree of freedom can be thought of as an SU(2) singlet (valence) bond between two spins, in resonating singlet valence plaquette (RSVP) physics, it corresponds to an SU(4) singlet comprising four sites; this might arise for example in a spin-orbital model. Here, we discuss the detailed phase diagram for the simplest case -- the Rokhsar-Kivelson RSVP model on the cubic lattice. [Preview Abstract] |
Wednesday, March 23, 2005 4:30PM - 4:42PM |
S9.00011: Introducing interactions in quantum dimer, vertex and loop models at the RK point Claudio Castelnovo, Claudio Chamon, Christopher Mudry, Pierre Pujol We present a generalized class of Rokhsar-Kivelson (RK) Hamiltonians that are in one-to-one correspondence with generic stochastic classical systems described by a Master equation in matrix form. We show that the ground state of the quantum system can be computed exactly and the zero-temperature phase diagram is captured by the phase diagram of the corresponding classical system at equilibrium. Moreover, the excitation spectrum over the ground state is given by the relaxation rates of the Master equation for the classical system. We then show how this framework allows to introduce interactions in known systems at the RK point, such as quantum dimer and vertex models, and to study phase transitions along lines of RK points. We also illustrate how one can construct exotic quantum Hamiltonians that are incapable of equilibrating to their ground state when coupled to a local thermal bath, and that exhibit relaxation time scales characteristic of a quantum glass. [Preview Abstract] |
Wednesday, March 23, 2005 4:42PM - 4:54PM |
S9.00012: Quantum glassiness in clean strongly correlated systems: an example of topological overprotection Claudio Chamon Describing matter at near absolute zero temperature requires understanding a system's quantum ground state and the low energy excitations around it, the quasiparticles, which are thermally populated by the system's contact to a heat bath. However, this paradigm breaks down if thermal equilibration is obstructed. I present solvable examples of quantum many-body Hamiltonians of systems that are unable to reach their ground states as the environment temperature is lowered to absolute zero. These examples, three dimensional generalizations of quantum Hamiltonians proposed for topological quantum computing, 1) have no quenched disorder, 2) have solely local interactions, 3) have an exactly solvable spectrum, 4) have topologically ordered ground states, and 5) have slow dynamical relaxation rates akin to those of strong structural glasses. [Preview Abstract] |
Wednesday, March 23, 2005 4:54PM - 5:06PM |
S9.00013: Frustrated corner-shared triangles: the B20 structure John Hopkinson, Hae-Young Kee We present a mean-field treatment of the classical Heisenberg model on the B20 lattice which is composed of two intertwined sublattices of corner-shared triangles. When one sublattice \{(x,x,x),(1/2+x,1/2-x,-x),cyclic perm.\} is magnetic we find a non-trivially degenerate ground state over a modified sphere. Addition of next nearest neighbor terms lifts this degeneracy leading to a host of long period magnetic structures--analogues of those shown by helimagnets--along the qqq or qq0 directions. The implications of these results for neutron scattering experiments will be discussed in light of recent surprising experiments under pressure on the itinerant MnSi, and renewed interest in the ``Kondo insulator'' FeSi and its doped semiconducting helimagnetic partner Co$_x$Fe$_{(1-x)}$Si. [Preview Abstract] |
Wednesday, March 23, 2005 5:06PM - 5:18PM |
S9.00014: Spin frustration controlled by orbital fluctuations Hiroaki Onishi, Takashi Hotta In order to clarify a key role of orbital degree of freedom in geometrically frustrated electron systems, we investigate an $e_{\rm g}$-orbital Hubbard model on a zigzag chain at quarter filling by using numerical techniques. When two orbitals are degenerate, orbital degree of freedom is active, but a $3x^2-r^ 2$ orbital is selectively occupied to suppress the spin frustration. Namely, the occupied orbital shape extends just along the direction of a double chain, and the zigzag chain is reduced to a double-chain spin system due to the spatial anisotropy of orbitals. On the other hand, taking account of the level splitting $\Delta$ between $3z^2-r^2$ and $x^2-y^2$ orbitals, electrons are forced to accommodate in the lower level. When the $3z^2-r^2$ orbital is fully occupied for large positive $\Delta$, the orbital anisotropy disappears in the $xy$ plane and the spin frustration revives. With increasing $\Delta$ from zero to large values, the orbital state gradually changes and the orbital fluctuation is found to be significant in the intermediate region. We will discuss the change in orbital structure and spin incommensurability. [Preview Abstract] |
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S9.00015: Impurity induced frustrations in a non-frustrated antiferromagnet Sasha Chernyshev, Shiu Liu Zn substitution for Cu in La$_2$CuO$_4$ is thought to be an ideal example for a simple site dilution of the antiferromagnetic $S=1/2$, square lattice non-frustrated nearest-neighbor Heisenberg model. We show that starting from the microscopic three-band Hubbard model one obtains quite different, counterintuitive result. Namely, the spinless impurity generates {\it frustrating} interactions around itself. This is because the oxygen orbitals around Zn impurity site can be still engaged in the virtual transitions which produce substantial superexchange interactions between the Cu spins {\it across} the impurity site. This effect can explain noticeable discrepancies between the experimental data and theoretical results for the simple site- diluted Heisenberg model. [Preview Abstract] |
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S9.00016: Random Bonds Effects in the Spin-$\frac{1}{2}$ Heisenberg Antifferomagnet on the Square Lattice Nicolas Laflorencie, Stefan Wessel, Andreas Laeuchli, Heiko Rieger In one dimension, it is well know that the spin-$\frac{1}{2}$ Heisenberg antiferromagnetic (AF) chain, governed by ${\mathcal{H}}_{1d}=\sum_{i} J_i {\vec{S}}_i \cdot {\vec{S}}_{i+1},$ is unstable against any strength of bond randomness [1]. The {\it{quasi}}-long-range-ordered phase is indeed destroyed $\forall \langle J_{i}^{2} \rangle \ne 0$ and then replaced by the so-called {\it{Random Singlet Phase}} [1]. Here, we adress the question of the two-dimensionnal case on the square lattice. When non-frustrating randomness in the AF exchanges is introduced, we show that the situation for the following Hamiltonian ${\mathcal{H}}_{2d}=\sum_{\langle i,j \rangle} J_{i,j} {\vec{S}}_i \cdot {\vec{S}}_{j}$, is completely different from the one dimensionnal case. In fact, the extreme robustness of the $T=0$ AF order parameter as well as the appearance of localized excitations with increasing disorder has been studied with the help of several theoretical tools: Exact Diagonalizations, modified Spin-Waves calculations and Quantum Monte Carlo simulations performed at extremely low temperature over thousands of disordered samples and for systems up to $32\times 32$. Our results also lead to more general consideration about Griffiths singularities in random quantum magnets.\\ $[1]$ D. S. Fisher, Phys. Rev. B {\bf 50}, 3799 (1994). [Preview Abstract] |
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