Plaquette Ordering In SU (4) Antiferromagnets (original) (raw)
Related papers
eb 2 00 2 Plaquette Ordering in SU ( 4 ) Antiferromagnets
2002
We use fermion mean field theory to study possible plaquette ordering in the antiferromagnetic SU(4) Heisenberg model. We find the ground state for both the square and triangular lattices to be the disconnected plaquette state. Our mean field theory gives a first order transition for plaquette ordering for the triangular lattice. Our results suggest a large number of low lying states.
Order and disorder in SU(N) simplex solid antiferromagnets
We study the structure of quantum ground states of simplex solid models, which are generalizations of the valence bond construction for quantum antiferromagnets originally proposed by Affleck, Kennedy, Lieb, and Tasaki (AKLT) [Phys. Rev. Lett. 59, 799 (1987)]. Whereas the AKLT states are created by application of bond singlet operators for SU(2) spins, the simplex solid construction is based on N-simplex singlet operators for SU(N) spins. In both cases, a discrete one-parameter family of translationally-invariant models with exactly solvable ground states is defined on any regular lattice, and the equal time ground state correlations are given by the finite temperature correlations of an associated classical model on the same lattice, owing to the product form of the wave functions when expressed in a CP^{N-1} coherent state representation. We study these classical companion models via a mix of Monte Carlo simulations, mean-field arguments, and low-temperature effective field theories. Our analysis reveals that the ground states of SU(4) edge- and SU(8) face-sharing cubic lattice simplex solid models are long range ordered for sufficiently large values of the discrete parameter, whereas the ground states of the SU(3) models on the kagome (2D) and hyperkagome (3D) lattices are always quantum disordered. The kagome simplex solid exhibits strong local order absent in its three-dimensional hyperkagome counterpart, a contrast that we rationalize with arguments similar to those leading to `order by disorder'.
Er2Ti2O7: Evidence of quantum order by disorder in a frustrated antiferromagnet
PHYSICAL REVIEW B, 2003
Er2Ti2O7 has been suggested to be a realization of the frustrated 111 XY pyrochlore lattice antiferromagnet, for which theory predicts fluctuation-induced symmetry breaking in a highly degenerate ground state manifold. We present a theoretical analysis of the classical model compared to neutron scattering experiments on the real material, both below and above TN =1.173(2) K. The model correctly predicts the ordered magnetic structure, suggesting that the real system has order stabilized by zero-point quantum fluctuations that can be modelled by classical spin wave theory. However, the model fails to describe the excitations of the system, which show unusual features. PACS numbers: 28.20.Cz, 75.25.+z An important aspect of condensed matter is the separation of energy scales, such that the minimization of one set of interactions may result in the frustration of another. A paradigm is the frustrated antiferromagnet, in which the local magnetic couplings between ions are frustrated by the crystal symmetry that the ions adopt. However, a systematic study of the rare earth pyrochlore titanates R 2 Ti 2 O 7 has shown that local antiferromagnetic bond frustration is neither a necessary, nor a sufficient condition for magnetic frustration 1,2,3,4,5 . Rather, it arises from the interplay, in the context of the crystal symmetry, of the principal terms in the spin Hamiltonian. In the case of R 2 Ti 2 O 7 , the main terms are single-ion anisotropy, exchange and dipolar coupling. Depending on the balance of these factors, one observes spin ice behavior (R = Ho, Dy) 1,2,3 , spin liquid behavior (R = Tb) 4 , and dipole induced partial order (R = Gd) 5 .
A model for a Heisenberg antiferromagnet on a pyrochlore lattice with exchange and dipole-dipole interactions is studied via mean-field theory. In treating the dipoles by use of the Ewald method, a soft (critical) mode with a unique ordering wave vector is selected for all strengths of the dipoledipole coupling. For weak dipoles a partially ordered, three sublattice spin structure (P state), with q ord = 1 2 1 2 1 2 , is selected. A fully ordered, four sublattice spin structure (F state), with q = 000, competes with the P state and becomes the stable structure as the temperature is reduced. Our results are compared against other theoretical calculations and connection to recent experimental results for Gd2Ti2O7 are discussed.
Physical review, 2022
We consider a model Hamiltonian with two SU(4) fermions per site on a square lattice, showing a competition between bilinear and biquadratic interactions. This model has generated interest due to possible realizations in ultracold atom experiments and existence of spin liquid ground states. Using a basis transformation, we show that part of the phase diagram is amenable to quantum Monte Carlo simulations without a sign problem. We find evidence for spin nematic and valence bond crystalline phases, which are separated by a weak first order phase transition. A U(1) symmetry is found to emerge in the valence bond crystal histograms, suggesting proximity to a deconfined quantum critical point. Our results are obtained with the help of a loop algorithm which allows large-scale simulations of bilinear-biquadratic SO(N) models on arbitrary lattices in a certain parameter regime.
Static magnetic order on the triangular lattice in with
Physica B: Condensed Matter, 2009
In spite of numerous experimental and theoretical reports on LiNiO 2 , due to fundamental interest because its Ni 3þ ions form a triangular S ¼ 1 2 two-dimensional lattice, no consistent picture has emerged of the nature of its ground state. We have investigated the Li x NiO 2 system ð0:1pxp1Þ using muon-spin spectroscopy to gain further insight from the effects of varying the spin concentration. Static magnetic order, most likely to be incommensurate to the spatial lattice period, was found for xX0:6, while disordered magnetism due to localized Ni moments appears for x ¼ 1 2 À 1 4 , and, finally, Li 0:1 NiO 2 exhibits almost fully non-magnetic behavior. Combining the result of susceptibility measurements, the ground state of LiNiO 2 is thought to be a ''static but short-range'' A-type antiferromagnetic ordered system. That is, the Ni 3þ moments align ferromagnetically along the c-axis in the NiO 2 plane with an incommensurate modulation probably due to canting of the Ni 3þ moments, but antiferromagnetically between the adjacent NiO 2 planes.
Magnetic ordering in Gd 2 Sn 2 O 7 : the archetypal Heisenberg pyrochlore antiferromagnet
Journal of Physics: Condensed Matter, 2006
Low-temperature powder neutron diffraction measurements are performed in the ordered magnetic state of the pyrochlore antiferromagnet Gd 2 Sn 2 O 7 . Symmetry analysis of the diffraction data indicates that this compound has the ground state predicted theoretically for a Heisenberg pyrochlore antiferromagnet with dipolar interactions. The difference in magnetic structures of Gd 2 Sn 2 O 7 and of nominally analogous Gd 2 Ti 2 O 7 is found to be determined by a specific type of third-neighbor superexchange interaction on the pyrochlore lattice between spins across empty hexagons.
Colossal Effects in Transition Metal Oxides Caused by Intrinsic Inhomogeneities
Physical Review Letters, 2001
The influence of quenched disorder on the competition between ordered states separated by a firstorder transition is investigated. A phase diagram with features resembling quantum-critical behavior is observed, even using classical models. The low-temperature paramagnetic regime consists of coexisting ordered clusters, with randomly oriented order parameters. Extended to manganites, this state is argued to have a colossal magnetoresistance effect. A scale T ء for cluster formation is discussed. This is the analog of the Griffiths temperature, but for the case of two competing orders, producing a strong susceptibility to external fields. Cuprates may have similar features, compatible with the large proximity effect of the very underdoped regime.