Bulletin of the American Physical Society
APS March Meeting 2013
Volume 58, Number 1
Monday–Friday, March 18–22, 2013; Baltimore, Maryland
Session F15: Focus Session: New Frustrated Quantum States: Theory & Materials |
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Sponsoring Units: GMAG DMP Chair: Piers Coleman, Rutgers University Room: 317 |
Tuesday, March 19, 2013 8:00AM - 8:36AM |
F15.00001: Lattices of Magnetic Vortices in a Frustrated Mott Insulator Invited Speaker: Cristian Batista Chiral spin textures with different length scales emerge in some itinerant magnets and are attracting increasing interest in the study of magneto-transport and possible applications to magnetic data storage and spin-electronic devices. It is natural to ask if similar topological textures can emerge in Mott insulators and also lead to magneto-electric effects. In this talk I will show that this is indeed possible when the exchange interactions are geometrically frustrated. For this purpose, I will consider a frustrated S$=$1/2 XXZ Hamiltonian that is a low-energy effective model for Ba$_{\mathrm{3}}$Mn2O$_{\mathrm{8}}$, a novel layered spin-dimer compound, comprising magnetic dimers of Mn$^{\mathrm{5+}}$ ions arranged on triangular planes. Successive layers are stacked following an ABC sequence, such that the dimer units on adjacent planes are positioned in the center of the triangular plaquettes of the layers above and below. The effective exchange anisotropy of the low-energy model results from frustration between exchange interactions connecting the same pair of dimmers. The competition between intra and inter-layer exchange interactions leads to a triplon dispersion with six-fold degenerate minima at the incommensurate wave vectors $\pm $Q$_{n}$ (1$\le n\le $3). This degeneracy leads to a very rich quantum phase diagram near the magnetic field induced quantum critical point, that is constructed by adding ladder diagrams and minimizing the resulting energy functional. The phase diagram includes different multi-Q magnetic orderings, which combine up to the six degenerate incommensurate lowest-energy modes $\pm $Q$_{n}$ (1$\le n\le $3). In particular, it includes a six-Q state that consists of a lattice of magnetic vortices and other complex spin textures associated with different multi-Q ordered states. [Preview Abstract] |
Tuesday, March 19, 2013 8:36AM - 8:48AM |
F15.00002: Unconventional quantum critical points in the generalized quantum dimer models Zi-Xiang Li, Fan Yang, Hong Yao We study a class of generalized quantum dimer models with both NN and NNN dimers on the square lattice, whose exact ground state wave function can be constructed. By varying the weight of NNN dimers and the interactions between dimers, we obtain a rich quantum phase diagram which hosts quantum spin liquid phases and various valence bond solids. We then investigate the quantum critical behavior of the transitions between spin liquids and valence bond solids by analytically studying its effective field theory and numerically doing variational Monte Carlo simulations. We discuss unconventional quantum critical points in this system. [Preview Abstract] |
Tuesday, March 19, 2013 8:48AM - 9:00AM |
F15.00003: Supersolids and Anomalous Hysteresis in Frustrated Spin-Dimer Systems Daisuke Yamamoto, Ippei Danshita We study the ground-state properties of weakly coupled spin dimers on a triangular lattice. The competition of the two (direct and crossed) interdimer interactions and the geometry of the triangular lattice lead to a strong frustration. By using a large-size cluster mean-field method and the cluster-size scaling, we determine the quantitative magnetic phase diagram of the system under the presence of a magnetic field. The strong intradimer interaction provides a gapped spin-singlet ground state. If the magnetic field exceeds a certain critical value, the system undergoes a phase transition to a magnetically ordered state, which is known as a Bose-Einstein condensation (BEC) of spin-triplet excitations called ``triplons.'' We find that for strong magnetic fields, the magnetization curve shows plateaus at 1/3 and 2/3 of the total magnetization, in which the local singlet and triplet states form a superlattice pattern. This state can be regarded as a solid of triplons. We also find that if increasing (decreasing) the magnetic field from the 1/3 (2/3) plateau, the BEC of triplons occurs on the superlattice background, leading to the transition into ``magnon supersolid'' phase. The region of supersolid phase in the phase diagram is reasonably large compared to the square-lattice case. [Preview Abstract] |
Tuesday, March 19, 2013 9:00AM - 9:12AM |
F15.00004: Quantum spin-ordered states for the frustrated XY model on the honeycomb lattice Andrea Di Ciolo, Juan Carrasquilla, Federico Becca, Victor Galitski, Marcos Rigol We consider the frustrated XY model on the honeycomb lattice and determine the stability of several classical spin states supplemented with a long-range Jastrow factor that introduces quantum fluctuations. In particular, we focus on the competition between antiferromagnetic, collinear, and generic spiral order upon increase of frustration. Our investigation is based on Variational Monte Carlo calculations. [Preview Abstract] |
Tuesday, March 19, 2013 9:12AM - 9:24AM |
F15.00005: Evidence of valence bond condensation in the frustrated cluster magnet LiZn$_{2}$Mo$_{3}$O$_{8}$ John Sheckelton, James Neilson, Daniel Soltan, Tyrel McQueen The reduced molybdenum oxide LiZn$_{2}$Mo$_{3}$O$_{8}$ is a Mott insulating material built of two dimensional layers of magnetic Mo$_{3}$O$_{13}$ triangular clusters, arranged on a triangular lattice. Between these magnetic layers are disordered non-magnetic LiZn$_{2}$ layers. The formal oxidation state and calculations show each molybdenum cluster collectively produces a S$=$1/2 moment. The ``triangle of triangles'' arrangement of magnetic clusters gives rise to exciting frustrated magnetic physics while also preventing Jahn-teller instabilities and site disorder seen in single ion frustrated systems. In addition, the structure allows for facile electronic doping of the magnetic layers. Structural and measured physical properties and ongoing research will be discussed. The evidence discussed indicates the formation of an exotic condensed valence bond state, reminiscent of the long-sought resonating valence bond state. [Preview Abstract] |
Tuesday, March 19, 2013 9:24AM - 9:36AM |
F15.00006: LiZn$_2$Mo$_3$O$_8$: honeycomb spin liquid in a triangular lattice material? Rebecca Flint, Patrick Lee LiZn$_2$Mo$_3$O$_8$ is a S=1/2 triangular lattice material in which two-thirds of the spins vanish at 100K, while the remaining spins remain free down to the lowest temperatures. There is no thermodynamic phase transition, and does not appear to be any magnetic order. The experimental proposal is that the triangular lattice decouples into a honeycomb lattice with free spins in the center of each hexagon, however, it is not immediately clear what favors this decompostion. We argue that a set of alternating octahedral rotations can strengthen the bonds of the honeycomb lattice while weakening those to the central spin. Furthermore, if the honeycomb lattice forms a $Z_2$ spin liquid, as proposed for the $J_1-J_2$ Heisenberg model, instead of a N\'{e}el or valence bond solid state, the central spin can delocalize over the hexagon, further favoring this decomposition, and also stabilizing the spin liquid phase over the N\'{e}el and VBS phases. Experimentally, this proposal can be tested by searching for signatures of the octahedral rotations, which may be short range or dynamic, but should result in a $q=0$ soft phonon mode. The spinon spectrum of the gapped $Z_2$ spin liquid should also have signatures in inelastic neutron scattering. We also discuss possible 3D analogues. [Preview Abstract] |
Tuesday, March 19, 2013 9:36AM - 9:48AM |
F15.00007: ABSTRACT WITHDRAWN |
Tuesday, March 19, 2013 9:48AM - 10:00AM |
F15.00008: Improved cluster-effective-field study on frustrated quantum spin systems in 2D Yoshihiko Nonomura Although frustrated quantum spin systems in two dimensions are fascinating playground of novel quantum states, systematic numerical study with the quantum Monte Carlo method is difficult in such systems owing to the negative sign problem. Then, cluster-effective-field approach may be useful as an alternative numerical tool. Crucial points of formulation are to use periodic boundary clusters and to compare two different clusters. As an example, the $J_{1}$-$J_{2}$ model, where $S=1/2$ Heisenberg spins are located on a square lattice with the nearest-neighbor and next-nearest-neighbor antiferromagnetic couplings $J_{1}$ and $J_{2}$. Classical N\'eel or sublattice N\'eel orders become unstable in the vicinity of $J_{2}/J_{1}=0.5$, where novel quantum states are expected to be stable. When the $16$- and $20$-spin clusters are used and the columnar or staggered dimer orders are taken as order parameters, we have coexisting regions of magnetic and dimer orders and first-order phase transitions between the columnar and staggered dimer orders. Further results based on larger clusters and improved formulations including multi-body effective fields are also discussed in the presentation. [Preview Abstract] |
Tuesday, March 19, 2013 10:00AM - 10:12AM |
F15.00009: Theory of inelastic neutron scattering in a quantum spin nematic Nic Shannon, Andrew Smerald The idea that a quantum magnet could act like a liquid crystal, breaking spin-rotation symmetry without breaking time-reversal symmetry, holds an abiding fascination. However, despite being a viable form of magnetic order, None the less, experimental evidence for ``spin nematic'' states in magnetic insulators remains scarce. And the very fact that spin nematic states do not break time-reversal symmetry renders them ``invisible'' to the most common probes of magnetism --- they do {\it not} exhibit magnetic Bragg peaks, a static splitting of lines in NMR spectra, or oscillations in $\mu$SR. However, as a consequence of breaking spin-rotation symmetry, spin-nematic states {\it do} posses a characteristic spectrum of dispersing excitations which could be observed in inelastic neutron scattering. With this in mind, we develop a symmetry-based description of long-wavelength excitations in a broad class of spin-nematic states, based on an SU(3) generalisation of the quantum non-linear sigma model. We use this field theory to make explicit predictions for inelastic neutron scattering, and argue that the wave-like excitations it predicts could be used to identify the symmetries broken by the unseen spin-nematic order. [Preview Abstract] |
Tuesday, March 19, 2013 10:12AM - 10:24AM |
F15.00010: Gapless spin liquid phase in the J1-J2 Heisenberg model Wenjun Hu, Federico Becca, Sandro Sorella We study the stability of a Z2 spin liquid in the highly frustrated regime of the J1-J2 Heisenberg model in the square lattice, namely with nearest and next nearest antiferromagnetic superexchange interactions. We use state of the art quantum Monte Carlo methods[S. Sorella {\it et al.}, prl {\bf 88}, 117002 (2002)] and show that, by means of few Lanczos steps acting over our initial wave function, we can achieve basically exact energies for the ground state and the low lying spin excitations, whenever our results can be compared with exact diagonalization reference data. For large clusters we show evidence that our calculations remain very accurate because we can estimate exact eigenvalues by extrapolating our results to the exact zero variance limit. By taking into account these important corrections, our final phase diagram seems to be inconsistent with an opening of a sizable spin gap in the spin liquid region, as recently found by a DMRG study [H.-C. Jiang {\it et al.}, prl {\bf 86}, 024424 (2012)]. [Preview Abstract] |
Tuesday, March 19, 2013 10:24AM - 10:36AM |
F15.00011: Symmetric and nematic $Z_2$ quantum spin liquids: applications to the $J_1$-$J_2$ Heisenberg model Yifan Jiang, Fan Yang, Hong Yao We classify symmetric and nematic $Z_2$ quantum spin liquid states on the square lattice by analyzing bosonic PSG. We then compute the energies of various symmetric and nematic $Z_2$ spin liquid states for the $J_1$-$J_2$ square Heisenberg model by doing variational Monte Carlo simulations. The connections of our variational Monte Carlo studies with the recent DMRG results on the same model will also be discussed. [Preview Abstract] |
Tuesday, March 19, 2013 10:36AM - 10:48AM |
F15.00012: Deconfined Criticality in a $J-Q$ model on Honeycomb lattice Sumiran Pujari, Fabien Alet, Kedar Damle The Deconfined Criticality scenario\footnote{T. Senthil \emph{at al}, Science 303, 1490 (2004).} describes in the context of quantum magnets a generic non-Landau second-order transition between two orders that break different symmetries - antiferromagnetic order that breaks $SU(2)$ symmetry and Valence bond (VB) order breaking lattice translational symmetry. We investigate this physics in the context of a $J-Q$ model\footnote{A. W. Sandvik, Phys. Rev. Lett. 98, 227202 (2007).} on the honeycomb lattice using both $T=0$ Projector Quantum Monte Carlo (QMC) and finite-$T$ Stochastic Series Expansion QMC techniques. We find evidence for a continuous transition from different measurements including scaling of N\'eel and VB order parameters, Binder ratios of staggered magnetization, stiffness and uniform susceptibility. We have indications that this critical point belongs to the same universality class as the one observed on square lattice $J-Q$ model. Our results also suggest that this critical fixed point controlling deconfined critical behaviour remains essentially unchanged even on the honeycomb lattice which allows three-fold hedgehog defects in the N\'eel order to be present in the continuum description of the critical point. [Preview Abstract] |
Tuesday, March 19, 2013 10:48AM - 11:00AM |
F15.00013: Monte Carlo studies of spinon deconfinement in two dimensions Ying Tang, Anders Sandvik We have used a recently proposed quantum Monte Carlo algorithm [1] to study spinons (emergent $S=1/2$ excitations) in 2D Resonating-Valence-Bond (RVB) spin liquids and in a $J$-$Q$ model hosting a N\'eel--VBS phase transition at zero temperature. We found that spinons are well defined quasi-particles with finite intrinsic size in the RVB spin liquid. The distance distribution between two spinons show signatures of deconfinement. However, at the N\'eel--VBS transition, we found that the spinon size itself is comparable to the confinement length (the size of the bound state), even showing a shrinkage of the bound state (triplon) relative to the single spinon. Both the spinon size and the confinement length diverge as the critical point is approached. We attempt to extract the corresponding exponent. $[1]$ Y. Tang and A. W. Sandvik, Phys. Rev. Lett. {\bf 107}, 157201 (2011). [Preview Abstract] |
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