Bulletin of the American Physical Society
2008 APS March Meeting
Volume 53, Number 2
Monday–Friday, March 10–14, 2008; New Orleans, Louisiana
Session V27: Focus Session: Frustrated Theory |
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Sponsoring Units: GMAG Chair: Oleg Tchernyshyov, Johns Hopkins University Room: Morial Convention Center 219 |
Thursday, March 13, 2008 11:15AM - 11:27AM |
V27.00001: Path Integral Approach to Geometrically Frustrated Quantum Antiferromagnets Miraculous Bhaseen, John Chalker We develop a path integral approach to geometrically frustrated quantum antiferromagnets. Using Hubbard--Stratonovich transformations to decouple the interactions within clusters of spins, we establish a high temperature expansion of the quantum partition function. This semiclassical approach based on conjugate cluster variables allows us to descend below the Curie--Weiss temperature scale, and to describe the emergent spin liquid regime. We make contact with complementary approaches based on spin wave theory. [Preview Abstract] |
Thursday, March 13, 2008 11:27AM - 11:39AM |
V27.00002: Contractor-Renormalization approach to frustrated magnets in a magnetic field Andreas Abendschein, Sylvain Capponi We propose to use the Contractor Renormalization (CORE) technique in order to derive effective models for quantum magnets in a magnetic field. CORE is a powerful non-perturbative technique that can reduce the complexity of a given microscopic model by focusing on the low-energy part. We provide a detailed analysis of frustrated spin ladders which have been widely studied in the past: in particular, we discuss how to choose the building block and emphasize the use of their reduced density matrix. With a good choice of basis, CORE is able to reproduce the existence or not of magnetization plateaux in the whole phase diagram contrary to usual perturbation theory. Furthermore, we present recent results for other, potentially more interesting geometries like the Heisenberg bilayer where we also address the issue of plateau formation and point out the analogy between non-frustrated strongly anisotropic models and frustrated SU(2) ones. Finally, we investigate the magnetization curve of the Shastry-Sutherland model and, however in absence of a magnetic field, we consider the square lattice with four-spin ring-exchange. [Preview Abstract] |
Thursday, March 13, 2008 11:39AM - 11:51AM |
V27.00003: Spin-orbital liquid state on the square lattice with emergent Majorana fermions and Z$_2$ topological order Ashvin Vishwanath, Fa Wang Magnetism from d-electrons often retains orbital degeneracy which can enhance quantum fluctuations and lead to exotic liquid-like ground states with no conventional order. Indeed, experimental systems like LiNiO$_2$, FeSc$_2$S$_4$ etc. with orbital degeneracy show a lack of order down to low temperatures. We introduce a Majorana-fermion slave particle theory to study such states in spin-1/2 models with e$_g$ orbital degeneracy. This is first applied to a square lattice model with enhanced SU (4) symmetry. A mean field treatment predicts a spin-orbital liquid state with nodal Majorana fermion excitations and Z$_2$ topological order. A variational Monte-Carlo study of the corresponding wavefunction confirms the absence of magnetic order and bond order, which makes it a candidate state for a spin orbital liquid. Comparing against the exact diagonalization studies in [Bossche et al. Eur. Phys. J. B 17, 367 (2000)], our state is found to have significant overlap with the ground state on small lattices, despite the absence of a variational parameter. More realistic models with lower symmetry and on different lattices are analyzed within our formalism, and applications to S=3/2 atoms confined in optical lattices are pointed out. [Preview Abstract] |
Thursday, March 13, 2008 11:51AM - 12:27PM |
V27.00004: Magnetic monopoles in spin ices and spin excitations in other pyrochlores Invited Speaker: Exotic excitations go along with the unusual ground states of frustrated magnets. One of the most striking examples occurs in dipolar spin ice, where the dipole moment of the underlying electronic spin degrees of freedom fractionalises into magnetic monopoles. This constitutes possibly the first instance of fractionalisation in a three-dimensional material. It enables us to account for a mysterious phase transition observed experimentally in spin ice in a magnetic field, which is a liquid-gas transition of the magnetic monopoles. These monopoles can also be detected by other means, e.g., in an experiment modelled after the celebrated Stanford magnetic monopole search. We also discuss other instances of unusual pyrochlore excitations. [Preview Abstract] |
Thursday, March 13, 2008 12:27PM - 12:39PM |
V27.00005: Vortex Berry phases and the magnetization of quantum magnets Akihiro Tanaka, Keisuke Totsuka, Xiao Hu We revisit the magnetization process of quantum antiferromagnets subject to an external magnetic field, and show how an interpretation in terms of Berry phases emerges. First we develop a continuum variant of the Lieb-Schulz-Mattis- type approach to the 1d problem, and find that the well-known commensurability condition of Oshikawa et al derives from the Berry-connection theory of the crystal momentum of a magnet first suggested by Haldane. Building on the physical picture which arises from this analysis, we then go on to formulate an effective field theory which can deal with the higher dimensional cases. We show that a topological term associated with vortices of the XY-like slowly varying fields controls the behavior of the system. Finally we utilize this new framework to discuss possible occurrences of fractionalized states. [Preview Abstract] |
Thursday, March 13, 2008 12:39PM - 12:51PM |
V27.00006: Kinetic ferromagnetism on frustrated lattices Frank Pollmann, Kirill Shtengel, Peter Fulde Systems with frustrated interactions are generally characterized by a high density of low--lying excitations which can be responsible for interesting physical effects. Much attention has been paid to the effects of frustration in antiferromagnetic systems. In this talk, however, we present a model of ferromagnetism arising in a frustrated system. We study strongly correlated electrons described by an extended Hubbard Hamiltonian on a kagome lattice at 1/6 and 1/3 filling. In the limit $|t|\ll V\ll U$ (where $t$ is a hopping amplitude, $U$ is on-site repulsion and $V$ is nearest-neighbor repulsion), we derive an effective low-energy Hamiltonian for this model. The Perron-Frobenius theorem can then be used to show that the ground state of this system is ferromagnetic. We will also address the robustness of ferromagnetism to finite temperature effects and other interactions and discuss possible extensions to other lattices. [Preview Abstract] |
Thursday, March 13, 2008 12:51PM - 1:03PM |
V27.00007: Magnetic Fluctuations in the Hubbard Model on Kagome-based Frustrated Lattices Masafumi Udagawa, Yukitoshi Motome We report our results on the interplay between electron correlation and magnetic fluctuations in the geometrically-frustrated Kagome and hyper-Kagome Hubbard models at half filling. These models have two different geometrical units important in the low-energy physics: the frustrated triangle and the non-frustrated loop with even-number sites. In order to treat both of them on equal footing, we apply cluster dynamical mean-field theory to large-size clusters up to 12 sites. By calculating the spin susceptibility $\chi({\vec q}, \omega)$, we have found in the Kagome system that an anomalous one-dimensional magnetic correlation previously found near the Mott transition [1] is observed even in the non-interacting case at high temperature, and its temperature range gradually suppressed by increasing electron correlation. This behavior is ascribed to the nesting property at the van-Hove singularity preserved under electron correlation. We will also present the results for hyper-Kagome system in relation to the recent experiments on Na$_4$Ir$_3$O$_8$ [2]. \\ \noindent [1]\ T.\ Ohashi {\it et al.}, Phys.\ Rev.\ Lett.\ {\bf 97}, 066401 (2006)\\ \noindent [2]\ Y.\ Okamoto {\it et al.}, Phys.\ Rev.\ Lett.\ {\bf 99}, 137207 (2007) [Preview Abstract] |
Thursday, March 13, 2008 1:03PM - 1:15PM |
V27.00008: Study of the $U(1)-Z_4$ cross-over in 2D valance-bond-solids Jie Lou, Anders Sandvik We consider the 2D Heisenberg model in the overcomplete basis of valence bonds. By tuning matrix elements corresponding closely to the diagonal and off-diagonal terms in Rokhsar-Kivelson quantum dimer model, we show, using a projector quantum Monte Carlo technique, that there is a quantum phase transition into a valence-bond-solid (VBS) state. This system allows us to study the cross-over length-scale [1] associated with emergent U(1) symmetry of the VBS order parameter [2], which has up until now not been possible in other systems [3], where the VBS order is weaker and prohibitively large system sizes are needed to observe the stabilization of a manifestly $Z_4$-symmetric VBS. \break [1] J. Lou, A. W. Sandvik, and L. Balents, Arxiv:0704.1472. [2] T. Senthil, A. Vishwanath, L. Balents, S. Sachdev, and M. P. A. Fisher, Science \textbf{303}, 1490 (2004). [3] A. W. Sandvik, Phys. Rev. Lett {\bf 98}, 227202 (2007). [Preview Abstract] |
Thursday, March 13, 2008 1:15PM - 1:27PM |
V27.00009: Dimerized Bond-Disordered Quantum Spin Models and Harris Criterion Jonas Gustafsson, Daoxin Yao, Erica Carlson, Anders W. Sandvik We study several different realizations of dimerized bond disorder in the two-dimensional square-lattice S=1/2 Heisenberg model, by introducing strong and weak couplings, $J_s,J_w$, randomly, but in such a way that each spin belongs to one strong bond (a dimer). We study the ground-state phase transition occurring at a critical ratio $g_c=J_s/J_w$ for different ways of distributing the dimers: (a) randomly distributed as in the classical dimer model, whence the dimer-dimer correlation function follows a power law, $c(r) \sim r^{-2}$, and (b) the random plaquette (RP) model, where all dimers are first placed horizontally in columns and thereafter any plaquette with dimers is flipped with probability $p=1/2$ or $1/4$. Our calculations show that the Harris criterion for the relevance of disorder is not applicable to these models. In all cases, the disorder does not appear to change the universality class from that obtaining with a regular dimer arrangement. [Preview Abstract] |
Thursday, March 13, 2008 1:27PM - 1:39PM |
V27.00010: Spontaneous parity breaking of Dirac spin liquid in a magnetic field Ying Ran, Wing-Ho Ko, Patrick Lee, Xiao-Gang Wen The Dirac spin liquid was proposed to be the ground state of the spin-1/2 Kagome antiferromagnets. In a magnetic field, we show that the state with Fermi pocket is unstable to the Landau level (LL) state and the XY ordered state. We mainly focus on the fully gapped LL state, which breaks parity symmetry and thus supports a finite temperature phase transition. We discuss experimental signatures which can be used to detect the possible Dirac spin liquid phase in Herbertsmithite ZnCu$_3$(OH)$_6$Cl$_2$. [Preview Abstract] |
Thursday, March 13, 2008 1:39PM - 1:51PM |
V27.00011: Two-step spin flop transition in quantum spin ladders Toru Sakai, Kiyomi Okamoto It is well known that the antiferromagnet with easy-axis anisotropies exhibits a field-induced first-order phase transition, the so- called spin flop. In one-dimensional quantum spin systems, instead of it, a second-order phase transition occurs because of large quantum fluctuations[1]. Particularly the S=1 antiferromagnetic chain with the easy-axis single-ion anisotropy was revealed to exhibit two successive field-induced second-order transitions by our previous numerical analysis[2]. However, such transitions have not been obseved yet. Recently a two-step spin flop transition was observed in the spin ladder system IPA-CuCl$_3$[3], which has ferromagnetic rung coupling. In order to clarify the mechanism of the two-step field-induced transition, we investigate the anisotropic spin ladder using the numerical diagonalization and the finite-size scaling analysis. As a result, we revealed that two different field-induced second-order quantum phase transitions possibly occur. Several phase diagrams are also presented. In addition we discuss on a possible two-step spin flop in other materials[4] and some frustrated systems. [1] C. N. Yang and C. P. Yang, Phys. Rev. 151 (1966) 258. [2] T. Sakai, Phys. Rev. B 58 (1998) 6268. [3] T. Masuda et al, Phys. Rev. Lett. 96 (2006) 047210. [4] H. Miyasaka et al, Inorg. Chem. 42 (2003) 8203. [Preview Abstract] |
Thursday, March 13, 2008 1:51PM - 2:03PM |
V27.00012: Spin and Singlet Dynamics of the S=1/2 Quantum Kagome Antiferromagnet Andreas Lauchli, Claire Lhuillier The kagome Heisenberg antiferromagnet with spin 1/2 has been the topic of many theoretical investigations. Most of these focused on groundstate properties or were aiming at an explanation of the anomalous high density of singlet excitations. In this contribution we report on exact diagonalization studies concentrating on dynamical correlation functions. First the full dynamical spin structure factor $\mathcal{S}(\mathbf{q},\omega)$ on 36 sites has been obtained, showing a broad, rather incoherent spectral response, which furthermore seems to increase significantly at low energies. Then we discuss the time dependent spin autocorrelation function as well as dynamical dimer-dimer correlation functions. All these results combined point towards a highly fluctuating system, both in the singlet and the triplet channel. We conclude by a comparison with recent inelastic neutron scattering measurements on the Herbertsmithite and Volborthite compounds. [Preview Abstract] |
Thursday, March 13, 2008 2:03PM - 2:15PM |
V27.00013: Pseudo-Dirac Hamiltonians and Flux Phases of SU(N) magnets F.J. Burnell, S.L. Sondhi, R. Shankar The lattice Dirac Hamiltonian describes a particle hopping on a lattice in a particular background magnetic field. We present a family of hopping Hamiltonians in other background fields that generalize many aspects of the Dirac Hamiltonian to lines and planes of nodes. In our canonical case, hopping on the pyrochlore lattice gives rise to a half filled fermi surface that consists of four intersecting [111] lines. This spectrum is invariant under tetrahedral rotations, rather than all rotations as in the Dirac case, resulting in a more complex matrix anti-commutation structure. This structure arises in a large N treatment of the SU(N) Heisenberg model on the pyrochlore. [Preview Abstract] |
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