Bulletin of the American Physical Society
2009 APS March Meeting
Volume 54, Number 1
Monday–Friday, March 16–20, 2009; Pittsburgh, Pennsylvania
Session V31: Focus Session: Frustration Theory and Modeling |
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Sponsoring Units: GMAG Chair: Taner Yildirim, NIST Center for Neutron Research Room: 335 |
Thursday, March 19, 2009 8:00AM - 8:12AM |
V31.00001: Rotational symmetry breaking in Heisenberg model on triangular lattice Ryo Tamura, Naoki Kawashima We study a finite-temperature phase transition in the two-dimensional classical Heisenberg model on a triangular lattice with a ferromagnetic nearest-neighbor interaction $J_1$ and an antiferromagnetic third-nearest-neighbor interaction $J_3$ using Monte Carlo simulation. Apart from a trivial degeneracy corresponding to O(3) spin rotations, the ground state for $J_3\ne 0$ has a threefold degeneracy corresponding to 120 degree lattice rotations. We find that this model exhibits a phase transition with breaking of the three-fold symmetry when $J3=J1/3$ and that the transition is of the first order. [Preview Abstract] |
Thursday, March 19, 2009 8:12AM - 8:24AM |
V31.00002: Finite-size scaling in frustrated Heisenberg models Sasha Chernyshev, Steven White Numerical studies of the 2D frustrated antiferromagnets are hindered by the absence of large-scale quantum Monte Carlo methods and by large finite-size effects in other methods. Using the effective $\sigma$-model we demonstrate that the most significant finite-size effects can be eliminated by an appropriate choice of the cluster aspect ratio, allowing for much more precise estimates of observables already in small systems. We show that such a ``magic'' aspect ratio depends on the boundary conditions, with a simple and convenient choice being precisely the geometry optimal for the DMRG method. Combining the improved DMRG accuracy with the use of non-traditional clusters for rapidly converging finite-size scaling, we study the ordering in the square- and triangular-lattice Heisenberg models. We demonstrate the vanishing of the leading finite-size effect $\sim O(1/L)$ in the order parameter $M$ for the sequence of clusters with the ``magic'' aspect ratio ($L_x/L_y$ close to 2), in agreement with the effective $\sigma$-model. We determine the thermodynamic limit of $M$ for the square lattice with an error comparable to quantum Monte Carlo. For the triangular lattice, we verify the existence of three-sublattice magnetic order, and estimate the order parameter to be $M = 0.205(15)$. [Preview Abstract] |
Thursday, March 19, 2009 8:24AM - 8:36AM |
V31.00003: Classical and quantum dimers on the star lattice John Fjaerestad We show that dimer coverings on the star lattice (aka the 3-12, Fisher, expanded kagome or triangle-honeycomb lattice) have $Z_2$ arrow and pseudo-spin representations analogous to those for the kagome lattice, and use these to construct an exactly solvable quantum dimer model (QDM) with a Rokhsar-Kivelson (RK) ground state. This QDM, first discussed by Moessner and Sondhi from a different point of view, is the star-lattice analogue of a kagome-lattice QDM analyzed by Misguich et al. We discuss various properties of the classical equal-weight dimer model on the star lattice, most of which are related to those of the RK state. Using both the arrow representation and the fermionic path integral formulation of the Pfaffian method, we calculate the number of dimer coverings, dimer occupation probabilities, and dimer, vison, and monomer correlation functions. The results show unusual features similar to those of dimers on the kagome lattice. We also discuss some generalizations to general Fisher lattices and their ``reduced'' lattices (the kagome, squagome, and triangular-kagome lattice being examples of the latter). Ref.: J. O. Fjaerestad, arXiv:0811.3789 [Preview Abstract] |
Thursday, March 19, 2009 8:36AM - 9:12AM |
V31.00004: Spatially anisotropic Heisenberg kagome antiferromagnet Invited Speaker: We study the quasi-one-dimensional limit of the spin-1/2 quantum Heisenberg antiferromagnet on the kagome lattice. The lattice is divided into antiferromagnetic spin-chains (exchange $J$) that are weakly coupled via intermediate ``dangling'' spins (exchange $J'$). Using one-dimensional bosonization, renormalization group methods, and current algebra techniques the ground state is determined in the limit $J' \ll J$. We find that the dangling spins and chain spins form a spiral with $O(1)$ and $O(J'/J)$ static moments, respectively, atop of which the chain spins exhibit a smaller $O[(J'/J)^2]$ antiferromagnetically ordered component along the axis perpendicular to the spiral plane. We describe similarities and differences of our findings with other recent studies, based on semi-classical and large-N approaches. Critical comparison of quasi-one-dimensional kagome antiferromagnet with other quasi-one-dimensional models will be presented as well. [Preview Abstract] |
Thursday, March 19, 2009 9:12AM - 9:24AM |
V31.00005: Ordered States on the Kagome Antiferromagnetic Heisenberg Model Simeng Yan, Steven White We numerically study the spin 1/2 Kagome antiferromagnetic Heisenberg Model with DMRG techniques. Recently, Singh and Huse proposed a dimerized ground state with a 36 site unit cell. To test this proposal, we have simulated the system on clusters which favor this order. If the order was not found, this would disprove the proposal. However, the results do show the proposed order. The strength of the dimerization on the pinwheels is surprisingly strong, with $<$S $\cdot $ S$>$ taking values of -0.7J on the strong bonds and -0.1J on the weak. We also have studied the system on clusters with a cylindrical geometry to test for the presence of the order. [Preview Abstract] |
Thursday, March 19, 2009 9:24AM - 9:36AM |
V31.00006: Universality Classes of Dimerized Bond-Disordered Quantum Spin Models Jonas Gustafsson, Daoxin Yao, Erica Carlson, Anders Sandvik We study the dimerized bond disordered S=1/2 Heisenberg models on the square lattice. Each spin belongs to one strong bond (a dimer) by introducing strong and weak couplings, $J_s$, $J_w$. By means of quantum Monte Carlo simulations, we find two different universality classes for the random dimer model and the random plaquette model. The change of universality class may be associated with the cancellation of Berry phase. Furthermore, we study the dilution effect by setting some strong bonds to 0. [Preview Abstract] |
Thursday, March 19, 2009 9:36AM - 9:48AM |
V31.00007: Emergent multipolar spin correlations in a fluctuating spiral - The frustrated ferromagnetic S=1/2 Heisenberg chain in a magnetic field, Andreas Lauchli, Julien Sudan, Andreas Luscher We present the phase diagram of the frustrated ferromagnetic $S=1/2$ Heisenberg $J_1$-$J_2$ chain in a magnetic field, obtained by large scale exact diagonalizations and density matrix renormalization group simulations. A vector chirally ordered state, metamagnetic behavior and a sequence of spin-multipolar Luttinger liquid phases up to hexadecupolar kind are found. We provide numerical evidence for a novel locking mechanism, which can drive spiral states towards spin-multipolar phases, such as quadrupolar or octupolar phases. Our results also shed new light on previously discovered spin-multipolar phases in two-dimensional $S=1/2$ quantum magnets in a magnetic field. We conclude by presenting numerical results on the dynamical spin structure factor in the various phases which are valuable in identifying multipolar phases in experiments. [Preview Abstract] |
Thursday, March 19, 2009 9:48AM - 10:00AM |
V31.00008: Dynamically dominant excitations of string solutions in the antiferromagnetic Heisenberg chain in magnetic fields Masanori Kohno We investigate behaviors of dynamical structure factors in the spin-1/2 antiferromagnetic Heisenberg chain in magnetic fields, using Bethe-ansatz solutions. We uncover a well-defined continuum in $S^{+-}(k,\omega)$, which comes from 2-string solutions in the Bethe ansatz. It continuously connects the des Cloizeaux-Pearson mode in the zero-field limit and the bound state of overturned spins from the ferromagnetic state near the saturation field. Also, we give a natural interpretation to particles in magnetic fields, psinon and antipsinon, as those carrying fractional quantum numbers $S^z$=+1/2 and -1/2, respectively. We argue that not only psinons and antipsinons but also particles representing strings play important roles for dynamical properties of the antiferromagnetic Heisenberg chain in magnetic fields. We confirm the relevance of the present results to real materials through comparisons with experimental results. [Preview Abstract] |
Thursday, March 19, 2009 10:00AM - 10:12AM |
V31.00009: Interplay between interaction and (un)correlated disorder in Heisenberg spin-1/2 chains Frieda Dukesz, Marina Zilbergerts, Lea Santos We consider a Heisenberg spin-1/2 chain and study the interplay between the Ising interaction and on-site disorder, while keeping the hopping amplitude constant. Disorder is characterized by both: uncorrelated and long-range correlated random on-site energies. The level of delocalization, quantified by the number of principal components, is largest in clean systems with non-interacting particles. However, in the presence of uncorrelated disorder, delocalization becomes maximum for a non-zero value of the interaction amplitude. The inclusion of long-range correlated disorder may further extend two-particle states, but the effect decreases with the number of excitations and strength of the interaction, and may even be reversed, as shown for half-filled chains. Quantum correlations, determined by a global entanglement measure, present similar behavior, but the largest value appears for clean systems with interacting particles. [Preview Abstract] |
Thursday, March 19, 2009 10:12AM - 10:24AM |
V31.00010: Algebraic spin liquid in an exactly solvable spin model Hong Yao, Shou-Cheng Zhang, Steven Kivelson We have introduced an exactly solvable quantum spin-3/2 model on the square lattice. Its ground state is a spin liquid with half integer spin per unit cell. The fermionic excitations are gapless with a linear dispersion, while the topological ``vison'' excitations are gapped. Moreover, the massless Dirac fermions are stable against any small perturbations with time reversal symmetry. Thus, this model is, to the best of our knowledge, the first exactly solvable model whose ground state is an ``algebraic spin liquid'' with half integer spin per unit cell. [Preview Abstract] |
Thursday, March 19, 2009 10:24AM - 10:36AM |
V31.00011: Extended supersolid phase of frustrated hard-core bosons on a triangular lattice Fa Wang, Frank Pollmann, Ashvin Vishwanath We study a model of hard-core bosons with frustrated nearest-neighbor hopping ($t$) and repulsion ($V$) on the triangular lattice. We argue for a supersolid ground state in the large repulsion ($V\gg|t|$) limit where a dimer representation applies, by constructing a unitary mapping to the well understood unfrustrated hopping case. This generalized `Marshall sign rule' allows us to establish the precise nature of the supersolid order by utilizing a recently proposed dimer variational wavefunction, whose correlations can be efficiently calculated using the Grassmann approach. By continuity, a supersolid is predicted over the wide parameter range, $V>-2t>0$. This also establishes a simple phase diagram for the triangular lattice spin 1/2 XXZ antiferromagnet. [Preview Abstract] |
Thursday, March 19, 2009 10:36AM - 10:48AM |
V31.00012: A $\Gamma $-matrix generalization of the Kitaev model Hsiang-Hsuan Hung, Congjun Wu, Daniel Arovas We extend the Kitaev model defined for the Pauli-matrices to the Clifford algebra $\Gamma $-matrices by taking the 4$\times $4 representation as an example. In a 2D decorated square lattice, the ground state spontaneously breaks time-reversal symmetry and exhibits a topological phase transition. The topologically non-trivial phase carries gapless chiral edge modes along the sample boundary. In the 3D diamond lattice, the ground states can exhibit gapless 3D Dirac cone- like excitations and gapped topological insulating states. The generalizations to even higher rank $\Gamma $-matrices are also discussed. [Preview Abstract] |
Thursday, March 19, 2009 10:48AM - 11:00AM |
V31.00013: Dzyloshinskii-Moriya interactions in valence bond systems II Mayra Tovar, Kumar Raman, Kirill Shtengel We investigate the effect of Dzyaloshinskii-Moriya interactions on the low temperature magnetic susceptibility for a system whose low energy physics is dominated by short-range valence bonds (singlets). Our general perturbative approach is applied to specific models expected to be in this class, including the Shastry-Sutherland model of the spin-dimer compound SrCu$_2 $(BO$_3$)$_2$ and the antiferromagnetic Heisenberg model of the recently discovered $S=1/2$ kagome compound ZnCu$_3$(OH)$_6 $Cl$_2$. The central result is that a short-ranged valence bond phase, when perturbed with Dzyaloshinskii-Moriya interactions, will remain time-reversal symmetric in the absence of a magnetic field but the susceptibility will be nonzero in the zero temperature limit. Applied to ZnCu$_3$(OH)$_6$Cl$_2$, this model provides an avenue for reconciling experimental results, such as the lack of magnetic order and lack of any sign of a spin gap, with known theoretical facts about the kagome Heisenberg antiferromagnet. [Preview Abstract] |
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