Bulletin of the American Physical Society
APS March Meeting 2010
Volume 55, Number 2
Monday–Friday, March 15–19, 2010; Portland, Oregon
Session Z34: Focus Session: Frustrated and Low-D Magnetism -- Quantum Magnetism III |
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Sponsoring Units: DMP GMAG Chair: Sriram Shastry, University of California, Santa Cruz Room: E144 |
Friday, March 19, 2010 11:15AM - 11:27AM |
Z34.00001: Hall Effect of Spin Waves in Frustrated Magnets Satoshi Fujimoto Spin transport phenomena have been attracting much interest in connection with applications to spintronics as well as their fundamental relation with the notion of topologically-induced spin currents. The spin Hall effect in semiconductors and metals, which has been studied extensively, allows for topological interpretation in terms of the Berry phase, and in this sense, it has an origin similar to that of the intrinsic anomalous Hall effect of charge currents. On the other hand, it was shown by several authors that the topological Berry phase is also raised by spin textures, and the Hall effect occurs in itinerant electron systems coupled with a nontrivial spin texture. Here, we propose a possible analogue of this phenomenon for localized spin systems with no charge degrees of freedom. In this scenario, a longitudinal magnetic field gradient induces a spin Hall current carried by spin wave excitations; i.e. Hall effect of spin waves involving no charge degrees of freedom. Our argument is based on a semiclassical analysis of spin dynamics taking into account topological Berry-phase effects. We also present a realistic miscroscopic model of a frustrated magnet with non-coplanar order which exhibits the Hall effect of spin waves. [Preview Abstract] |
Friday, March 19, 2010 11:27AM - 11:39AM |
Z34.00002: Spin chirality and thermal Hall effect in quantum magnets Hosho Katsura, Naoto Nagaosa, Patrick Lee We theoretically study the thermal Hall effect in insulating quantum magnets [1]. In contrast to itinerant magnets, there are no charge degrees of freedom in the localized spin systems and hence the heat current is totally carried by charge-neutral objects such as magnons and spinons. We consider the effect of the coupling between the scalar chirality and external magnetic fields or the effect of the Dzyaloshinskii-Moriya interaction which is related to the vector spin chirality, and find two distinct classes of thermal Hall responses. For ordered magnets, the intrinsic thermal Hall effect for magnons arises if the lattice geometry and the magnetic order satisfy certain conditions. A TKNN-type formula for the thermal Hall conductivity is also obtained. For a spin liquid, the thermal Hall effect for spinons due to the ``Lorentz force'' is expected if the spinons are deconfined. These results offer a new experimental method to study the ground state and low energy excitations in quantum magnets using thermal transport measurements. [1] H. Katsura, N. Nagaosa, and P. A. Lee, arXiv:0904.3427[cond-mat.str-el]. [Preview Abstract] |
Friday, March 19, 2010 11:39AM - 11:51AM |
Z34.00003: Entanglement spectrum of a topological phase in one dimension Frank Pollmann, Ari Turner, Erez Berg, Masaki Oshikawa We propose a scheme to classify gapped phases of one dimensional systems in terms of properties of the entanglement spectrum. We show that the Haldane phase of $S=1$ chains is characterized by a double degeneracy of the entanglement spectrum which is protected by any one of the following three symmetries: (i) the dihedral group of $\pi$-rotations about $x,y$ and $z$ axes; (ii) time-reversal symmetry $S^{x,y,z} \rightarrow - S^{x,y,z}$; (iii) link inversion symmetry. The degeneracy cannot be lifted unless either a phase boundary to another, ``topologically trivial'', phase is crossed, or the symmetry is broken. Physically, the degeneracy of the entanglement spectrum can be observed by adiabatically weakening a bond to zero, which leaves the two disconnected halves of the system in a finitely entangled state. [Preview Abstract] |
Friday, March 19, 2010 11:51AM - 12:03PM |
Z34.00004: Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice Zi Yang Meng, Stefan Wessel, Alejandro Muramatsu, Thomas Lang, Fakher Assaad Using projective (${T=0}$) quantum Monte Carlo simulations, we investigate the ground-state properties of the half-filled Hubbard model on the honeycomb lattice. We provide evidence for a gapped phase separating the weak-coupling semi-metal and the antiferromagnetically ordered phase at strong coupling. Exploring quasi-particle and spin excitation gaps, flux quantization as well as probing for various correlation functions, we conclude that in this intermediate interaction region the system exhibits no long-range magnetic or bond-order nor superconductivity. Several proposals on novel phases in related models have been put forward, whereas our simulations establish a spin liquid - even in the absence of magnetic frustration. [Preview Abstract] |
Friday, March 19, 2010 12:03PM - 12:15PM |
Z34.00005: Spin Bose-Metal phase in a spin-1/2 model with ring exchange on ladders M. Block, D.N. Sheng, Olexei I. Motrunich, Matthew P.A. Fisher I will discuss recent developments in the study of a 2D quantum phase of strongly correlated spins, the Spin Bose-Metal (SBM), a spin liquid characterized by gapless excitations residing on surfaces in momentum space (i.e. ``Bose surfaces''). Thus far, significant progress has been made by considering a triangular lattice Heisenberg model with a four-site ring exchange term on a 2-leg strip (see [1]), where quasi-1D signatures of the parent 2D phase can be detected (i.e. ``Bose points''). The ladder systems have provided a fruitful scaffolding for the implementation of the quasi-exact numerical method DMRG, as well as a theoretical approach via slave particles and Bosonization. To test the theory numerically, variational Monte Carlo (VMC) is employed with Gutzwiller projected products of Slater determinants as a direct comparison with DMRG results. Here, I will present new results for 3- and 4-leg ladders as we continue to drive towards two dimensions where this phase is potentially relevant in the study of organic Mott insulators near the metal-insulator transition. Indeed, we will offer evidence that the phase diagram of the 4-leg triangular ladder contains a Spin Bose-Metal phase. [1] D. N. Sheng \emph{et al}., Phys. Rev. B {\bf 79}, 205112 (2009). [Preview Abstract] |
Friday, March 19, 2010 12:15PM - 12:27PM |
Z34.00006: $d$-wave correlated Bose liquid phases on multi-leg ladders with ring exchange R. V. Mishmash, M. Block, Ribhu K. Kaul, D. N. Sheng, Olexei I. Motrunich, Matthew P. A. Fisher We discuss recent progress on the study of ladder descendants of a novel two-dimensional quantum phase of bosons moving on the square lattice which is characterized by singular surfaces in momentum space, namely the $d$-wave correlated Bose liquid (DBL). Using a combination of numerics (e.g., density matrix renormalization group, variational Monte Carlo, and exact diagonalization) and analytics (e.g., bosonization of a compact U(1) lattice gauge theory) we explore the existence and stability of ladder analogs of the DBL on $N$-leg ladders, with $N\ge3$, in the context of a model of itinerant hard-core bosons with frustrating four-site ring exchange. As in the case of $N=2$, see [1], we find numerical evidence for various strong-coupling DBL phases which can rather remarkably be understood within a slave-fermion picture in which the boson wave function is written as a product of two Slater determinants. The additional features and difficulties associated with taking $N>2$ will be addressed. The boson ring model we consider has potential physical realizations in the contexts of low-dimensional frustrated quantum magnets and in ultracold quantum gases. [1] D. N. Sheng \emph{et al.}, Phys. Rev. B {\bf 78}, 054520 (2008). [Preview Abstract] |
Friday, March 19, 2010 12:27PM - 12:39PM |
Z34.00007: Frustrated Orbital Exchange Models in p-band Mott Insulators Congjun Wu We investigate the general structure of orbital exchange physics in Mott-insulating states of p-orbital systems. Orbital orders occur in both the triangular and kagome lattices. In contrast, orbital exchange in the honeycomb lattice is frustrated as described by a novel quantum 120$^{\circ}$ model. Its classical ground states are mapped into configurations of the fully packed loop model with an extra U(1) rotation degree of freedom. Quantum orbital fluctuations select a six-site plaquette ground state ordering pattern in the semiclassical limit from the ``order from disorder'' mechanism. This effect arises from the appearance of a zero energy flat band of orbital excitations. [Preview Abstract] |
Friday, March 19, 2010 12:39PM - 12:51PM |
Z34.00008: A quantum liquid with deconfined fractional excitations in three dimensions Nic Shannon, Olga Sikora, Frank Pollmann, Karlo Penc, Peter Fulde Excitations which carry ``fractional'' quantum numbers are known to exist in one dimension in polyacetylene, and in two dimensions, in the fractional quantum Hall effect. Fractional excitations have also been invoked to explain the breakdown of the conventional theory of metals in a wide range of three-dimensional materials. However the existence of fractional excitations in three dimensions remains highly controversial. Here we report direct numerical evidence for the existence of an extended quantum liquid phase supporting fractional excitations in a concrete, three-dimensional microscopic model --- the quantum dimer model on a diamond lattice [1]. We demonstrate explicitly that the energy cost of separating fractional monomer excitations vanishes in this liquid phase, and that its energy spectrum matches that of the Coulomb phase in $(3+1)$ dimensional quantum electrodynamics [2,3]. \\[4pt] [1] O. Sikora {\it et al.} arXiv:0901.1057v3 --- to appear in Phys. Rev. Lett. \\[0pt] [2] R. Moessner and S.L. Sondhi, Phys. Rev. B {\bf 68}, 184512 (2003).\\[0pt] [3] D.L. Bergman {\it et al.} Phys. Rev. B {\bf 73}, 134402 (2006). [Preview Abstract] |
Friday, March 19, 2010 12:51PM - 1:03PM |
Z34.00009: projective construction of spin nematic states in S=1/2 frustrated ferromagnets Ryuichi Shindou, Tsutomu Momoi An $SU(2)$ slave-boson formulation of bond-type spin nematic orders is developed in the context of quantum frustrated ferromagnets, where the spin nematic states are described as the resonating spin-triplet valence bond (RVB) states. Namely, the $d$-vector of the spin-triplet pairing ansatz plays the role of the so-called `director' in the spin nematic states. The low-energy excitations around such bond-type spin quadrupolar orders generally comprise the gauge boson, massless goldstone bosons, spinon individual excitations and their composites. Using the projective symmetry-group arguments, we will argue how to identify the number of massless gauge bosons. Applying this formulation, we will next enumerate possible `mixed' RVB ansatzes in the $S=\frac{1}{2}$ $J_1$-$J_2$ Heisenberg model on the square lattice ($J_1$ ferromagnetic nearest neighbor and $J_2$ antiferromagnetic next nearest neighbor), and argue their stability against gauge fluctuations. As a result, we found two stable ansatzes in the intermediate coupling region, $J_1:J_2=1:0.4$. One is the $Z_2$ `Balian-Werthamer (BW)' state stabilized by the Higgs mechanism. The other is the $SU(2)$ `chiral $p$-wave' state, where the massless gauge fluctuations are controlled by the Chern-Simon mechanism. Especially, the former $Z_2$ state exhibits the same spatial configuration of the spin quadrupolar moment as found in the previous exact diagonalization studies. [Preview Abstract] |
Friday, March 19, 2010 1:03PM - 1:15PM |
Z34.00010: Competing quantum paramagnetic ground states of the Heisenberg antiferromagnet on the star lattice Bohm-Jung Yang, Arun Paramekanti, Yong Baek Kim We investigate various competing paramagnetic ground states of the Heisenberg antiferromagnet on the two dimensional star lattice which exhibits geometric frustration. Using slave particle mean field theory combined with a projective symmetry group analysis, we examine a variety of candidate spin liquid states on this lattice, including chiral spin liquids, spin liquids with Fermi surfaces of spinons, and nematic spin liquids which break lattice rotational symmetry. Motivated by connection to large-N SU(N) theory as well as numerical exact diagonalization studies, we also examine various valence bond solid (VBS) states on this lattice. Based on a study of energetics using Gutzwiller projected states, we find that a fully gapped spin liquid state is the lowest energy spin liquid candidate for this model. We also find, from a study of energetics using Gutzwiller projected wave functions and bond operator approaches, that this spin liquid is unstable towards two different VBS states --- a VBS state which respects all the Hamitonian symmetries and a VBS state which exhibits $\sqrt{3}\times\sqrt{3}$ order --- depending on the ratio of the Heisenberg exchange couplings on the two inequivalent bonds of the lattice. We compute the triplon dispersion in both VBS states within the bond operator approach and discuss possible implications of our work for future experiments on candidate materials. [Preview Abstract] |
Friday, March 19, 2010 1:15PM - 1:27PM |
Z34.00011: Fermionic mean field theory for arbitrary spin and Spin-1 algebraic spin liquid on triangle lattice Zheng-Xin Liu, Yi Zhou, Tai-Kai Ng We generalized the fermionic representation for Heisenberg model with spin-1/2 to arbitrary spin. The particle-hole symmetry for spin-1/2 Hilbert space is absent for $S\geq1$. We find a Lagrangian for Heisenberg model with spin-1 or spin-3/2 with restored particle-hole symmetry and study the corresponding mean fields. The excitation spectrum is gapped for the former and gapless for the latter, which is consistent with Haldane's conjecture. We also study the magnetic insulator $\mathrm{NiGa_2S_4}$ by applying the fermionic mean field theory to the spin-1 $J_1$-$J_3$-$K$ model $H=\sum_{\langle i,j\rangle} \left[J_1\mathbf S_i\cdot\mathbf S_j+K(\mathbf S_i\cdot\mathbf S_j)^2\right]+ J_3\sum_{[ i,j']}\mathbf S_i\cdot \mathbf S_{j'}$. We find two spin liquid solutions with gapless spinon excitations, which has never been discussed in literature to our knowledge. We assume that the ground state is in one of these spin liquid phases, then the gapless excitation spectrum explains the $T^2$ law of the specific heat at low temperature. The susceptibility calculated from the mean field theory is linear in T at low temperature. We attribute the experimentally observed nonzero susceptibility at zero temperature and the partially spin freezing below $T_f$ to the defects such as impurities or surface effects. [Preview Abstract] |
Friday, March 19, 2010 1:27PM - 1:39PM |
Z34.00012: Functional renormalization group study of charge and spin orders of the extended Hubbard model in frustrated lattices Hirokazu Takashima, Sumio Ishihara In order to study for novel spin and charge orders in strongly correlated electron systems in frustrated lattices,we investigated extended Hubbard model in 2 dimensional (2D) checkerboard and triangular lattices using the functional renormalization group method(fRG) with an improved algorithm [1]. In this method, both the quantum effect and the geometrical frustration effect at finite temperature are taken into account properly. Non-monotonic temperature dependence of the spin susceptibility was observed both in the models . In a 2D isotropic triangular lattice at half-filling, divergence of the particle-particle channel vertex functions was observed in a region of the intermediate value of the on-site Coulomb interaction. We have also investigated the extended Hubbard model with long-range Coulomb interactions. A possibility of the ferromagnetic order and calculations with including the self-energy correction will be introduced .[1] H. Takashima, R. Arita, K. Kuroki, and H. Aoki, J. Phys.: Conf. Ser, \textbf{150, }052261 (2009) [Preview Abstract] |
Friday, March 19, 2010 1:39PM - 1:51PM |
Z34.00013: Phase diagram of the SU(N) Hubbard-Heisenberg model on the honeycomb lattice Thomas C. Lang, Fakher F. Assaad, Zi Yang Meng, Stefan Wessel, Alejandro Muramatsu We present a projective ${T=0}$ quantum Monte-Carlo study of the ground-state properties of the the SU($N$) Hubbard Heisenberg model on hexagonal lattices up to ${18 \times 18}$ unit cells. The phase diagram is mapped out for increasing many body correlations from the large-$N$ limit to SU(2) for even $N$. It is shown that for all SU($N$) symmetric realizations, the model undergoes a quantum phase transition from a semimetal to an insulator for large values of $J/t$. While for ${N \ge 4}$ the insulating state is a valence bond crystal the SU(2) Hubbard Heisenberg model exhibits a gapped short range resonating valence bond phase separating the semimetal and an antiferromagnetic insulator. At SU(2) we reproduce the intermediate spin liquid phase found recently in the SU(2) Hubbard model on the hexagonal lattice. [Preview Abstract] |
Friday, March 19, 2010 1:51PM - 2:03PM |
Z34.00014: Quantum phase transition of the Hubbard model on a honeycomb lattice Ara Go, Kwon Park, Gun Sang Jeon We consider the Hubbard model on a honeycomb lattice at zero temperature. Within the cellular dynamical mean-field theory we study the quantum phase transition in the system. The antiferromagnetic transition, which is driven by the increase of the local interaction, is demonstrated by the staggered magnetization. We also examine the spectral properties of the system. The results are discussed in comparison with earlier works. [Preview Abstract] |
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