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Leon Balents - One of the best experts on this subject based on the ideXlab platform.

  • Degenerate perturbation theory of quantum fluctuations in a pyrochlore antiferromagnet
    Physical Review B, 2007
    Co-Authors: Doron L. Bergman, Ryuichi Shindou, Gregory A. Fiete, Leon Balents
    Abstract:

    We study the effect of quantum fluctuations on the half-polarized magnetization plateau of a pyrochlore antiferromagnet. We argue that an expansion around the easy Axis Limit is appropriate for discussing the ground state selection amongst the classically degenerate manifold of collinear states with a 3:1 ratio of spins parallel/anti-parallel to the magnetization Axis. A general approach to the necessary degenerate perturbation theory is presented, and an effective quantum dimer model within this degenerate manifold is derived for arbitrary spin $s$. We also generalize the existing semiclassical analysis of Hizi and Henley [Phys. Rev. B {\bf 73}, 054403 (2006)] to the easy Axis Limit, and show that both approaches agree at large $s$. We show that under rather general conditions, the first non-constant terms in the effective Hamiltonian for $s\geq 1$ occur only at {\sl sixth} order in the transverse exchange coupling. For $s\geq 3/2$, the effective Hamiltonian predicts a magnetically ordered state. For $s\leq 1$ more exotic possibilities may be realized, though an analytical solution of the resulting quantum dimer model is not possible.

  • Numerical evidences of fractionalization in an easy-Axis two-spin heisenberg antiferromagnet.
    Physical review letters, 2005
    Co-Authors: Donna Sheng, Leon Balents
    Abstract:

    Based on exact numerical calculations, we show that the generalized kagome spin model in the easy-Axis Limit exhibits a spin liquid, topologically degenerate ground state over a broad range of phase space, including a point at which the model is equivalent to a Heisenberg model with purely two-spin exchange interactions. We further present an explicit calculation of the gap (and dispersion) of ``vison'' excitations, and exponentially decaying spin and vison two-point correlators. These are hallmarks of deconfined, fractionalized, and gapped spinons. The nature of the phase transition from the spin-liquid state to a magnetic ordered state tuned by a negative four-spin ``potential'' term is also discussed in light of the low energy spectrum. These results greatly expand the range and the theoretical view of the spin-liquid phase in the vicinity of the Rokhsar and Kivelson exactly soluble point.

  • Fractionalization in an easy-Axis Kagome antiferromagnet
    Physical Review B, 2002
    Co-Authors: Leon Balents, Matthew P. A. Fisher, Steven Girvin
    Abstract:

    We study an antiferromagnetic spin-1/2 model with up to third nearest-neighbor couplings on the Kagome lattice in the easy-Axis Limit, and show that its low-energy dynamics are governed by a four site XY ring exchange Hamiltonian. Simple “vortex pairing” arguments suggest that the model sustains a novel fractionalized phase, which we confirm by exactly solving a modification of the Hamiltonian including a further four-site interaction. In this Limit, the system is a featureless “spin liquid”, with gaps to all excitations, in particular: deconfined S z = 1/2 bosonic “spinons” and Ising vortices or “visons”. We use an Ising duality transformation to express vison correlators as non-local strings in terms of the spin operators, and calculate the string correlators using the ground state wavefunction of the modified Hamiltonian. Remarkably, this wavefunction is exactly given by a kind of Gutzwiller projection of an XY ferromagnet. Finally, we show that the deconfined spin liquid state persists over a finite range as the additional four-spin interaction is reduced, and study the effect of this reduction on the dynamics of spinons and visons. It has now been almost 15 years since P.W. Anderson suggested that two-dimensional (2d) spin one-half antiferromagnets might condense into a featureless “spin liquid” quantum ground state 1 . In close analogy with the one-dimensional Heisenberg antiferromagnetic chain, the 2d spin liquid was posited to support deconfined spinon excitations – “particles” carrying s=1/2 in stark contrast with the s=1 triplet excitations of more familiar non-magnetic phases such as the spin-Peierls state

Yunfeng Zhang - One of the best experts on this subject based on the ideXlab platform.

  • Cutter selection for 5-Axis milling of sculptured surfaces based on accessibility analysis
    International Journal of Production Research, 2006
    Co-Authors: Yunfeng Zhang
    Abstract:

    Cutter selection is an important issue in process planning for 5-Axis milling of sculptured surfaces. To select the optimal cutter (from a set of available ones) to machine a given sculptured surface, it is essential to check whether a cutter is able to finish the entire surface without any interference. It is, therefore, necessary to check the accessibility of a cutter at any point on the surface. In this paper, the issues involved in cutter accessibility checking at a point are studied and corresponding checking methods have been developed. A search algorithm has been developed that is able to find the accessible posture range for a given cutter in terms of the tilting and rotational angles. The constraints considered in cutter accessibility analysis include the machine's Axis Limit, local-gouging, rear-gouging, and global-collision. This point-based solution is then extended to cover the whole surface by discretising the surface. In order to reduce the heavy computation in the checking procedure for th...

Steven Girvin - One of the best experts on this subject based on the ideXlab platform.

  • Fractionalization in an easy-Axis Kagome antiferromagnet
    Physical Review B, 2002
    Co-Authors: Leon Balents, Matthew P. A. Fisher, Steven Girvin
    Abstract:

    We study an antiferromagnetic spin-1/2 model with up to third nearest-neighbor couplings on the Kagome lattice in the easy-Axis Limit, and show that its low-energy dynamics are governed by a four site XY ring exchange Hamiltonian. Simple “vortex pairing” arguments suggest that the model sustains a novel fractionalized phase, which we confirm by exactly solving a modification of the Hamiltonian including a further four-site interaction. In this Limit, the system is a featureless “spin liquid”, with gaps to all excitations, in particular: deconfined S z = 1/2 bosonic “spinons” and Ising vortices or “visons”. We use an Ising duality transformation to express vison correlators as non-local strings in terms of the spin operators, and calculate the string correlators using the ground state wavefunction of the modified Hamiltonian. Remarkably, this wavefunction is exactly given by a kind of Gutzwiller projection of an XY ferromagnet. Finally, we show that the deconfined spin liquid state persists over a finite range as the additional four-spin interaction is reduced, and study the effect of this reduction on the dynamics of spinons and visons. It has now been almost 15 years since P.W. Anderson suggested that two-dimensional (2d) spin one-half antiferromagnets might condense into a featureless “spin liquid” quantum ground state 1 . In close analogy with the one-dimensional Heisenberg antiferromagnetic chain, the 2d spin liquid was posited to support deconfined spinon excitations – “particles” carrying s=1/2 in stark contrast with the s=1 triplet excitations of more familiar non-magnetic phases such as the spin-Peierls state

Matthew P. A. Fisher - One of the best experts on this subject based on the ideXlab platform.

  • Strong-coupling phases of frustrated bosons on a two-leg ladder with ring exchange
    Physical Review B, 2008
    Co-Authors: D. N. Sheng, Olexei I. Motrunich, Simon Trebst, Emanuel Gull, Matthew P. A. Fisher
    Abstract:

    Based on exact numerical calculations, we show that the generalized kagome spin model in the easy-Axis Limit exhibits a spin liquid, topologically degenerate ground state over a broad range of phase space, including a point at which the model is equivalent to a Heisenberg model with purely two-spin exchange interactions. We further present an explicit calculation of the gap (and dispersion) of ???vison??? excitations, and exponentially decaying spin and vison two-point correlators. These are hallmarks of deconfined, fractionalized, and gapped spinons. The nature of the phase transition from the spin-liquid state to a magnetic ordered state tuned by a negative four-spin ???potential??? term is also discussed in light of the low energy spectrum. These results greatly expand the range and the theoretical view of the spin-liquid phase in the vicinity of the Rokhsar and Kivelson exactly soluble point

  • Fractionalization in an easy-Axis Kagome antiferromagnet
    Physical Review B, 2002
    Co-Authors: Leon Balents, Matthew P. A. Fisher, Steven Girvin
    Abstract:

    We study an antiferromagnetic spin-1/2 model with up to third nearest-neighbor couplings on the Kagome lattice in the easy-Axis Limit, and show that its low-energy dynamics are governed by a four site XY ring exchange Hamiltonian. Simple “vortex pairing” arguments suggest that the model sustains a novel fractionalized phase, which we confirm by exactly solving a modification of the Hamiltonian including a further four-site interaction. In this Limit, the system is a featureless “spin liquid”, with gaps to all excitations, in particular: deconfined S z = 1/2 bosonic “spinons” and Ising vortices or “visons”. We use an Ising duality transformation to express vison correlators as non-local strings in terms of the spin operators, and calculate the string correlators using the ground state wavefunction of the modified Hamiltonian. Remarkably, this wavefunction is exactly given by a kind of Gutzwiller projection of an XY ferromagnet. Finally, we show that the deconfined spin liquid state persists over a finite range as the additional four-spin interaction is reduced, and study the effect of this reduction on the dynamics of spinons and visons. It has now been almost 15 years since P.W. Anderson suggested that two-dimensional (2d) spin one-half antiferromagnets might condense into a featureless “spin liquid” quantum ground state 1 . In close analogy with the one-dimensional Heisenberg antiferromagnetic chain, the 2d spin liquid was posited to support deconfined spinon excitations – “particles” carrying s=1/2 in stark contrast with the s=1 triplet excitations of more familiar non-magnetic phases such as the spin-Peierls state

B. W. Southern - One of the best experts on this subject based on the ideXlab platform.

  • Is there a phase transition in the isotropic Heisenberg anti-ferromagnet on the triangular lattice?
    Canadian Journal of Physics, 2001
    Co-Authors: W. Stephan, B. W. Southern
    Abstract:

    The phase diagram of the classical anisotropic (XXZ) Heisenberg model on the two-dimensional triangular lattice is investigated using Monte Carlo methods. In the easy-Axis Limit, two finite-temperature vortex-unbinding transitions have been observed. In the easy-plane Limit, there also appear to be two distinct finite-temperature phase transitions that are very close in temperature. The upper transition corresponds to an Ising-like chirality ordering and the lower temperature transition corresponds to a Kosterlitz–Thouless vortex-unbinding transition. These phase-transition lines all meet at the Heisenberg point and provide strong evidence that the isotropic model undergoes a novel finite-temperature phase transition. PACS Nos.: 75.10Hk, 75.40Mg

  • Is There a Phase Transition in the Isotropic Heisenberg Antiferromagnet on the Triangular Lattice
    Canadian Journal of Physics, 2001
    Co-Authors: W. Stephan, B. W. Southern
    Abstract:

    The phase diagram of the classical anisotropic (XXZ) Heisenberg model on the 2-dimensional triangular lattice is investigated using Monte Carlo methods. In the easy-Axis Limit, two finite temperature vortex unbinding transitions have been observed. In the easy-plane Limit, there also appear to be two distinct finite temperature phase transitions. The upper transition corresponds to an Ising-like chirality ordering and the lower temperature transition corresponds to a Kosterlitz-Thouless vortex unbinding transition. These phase transition lines all meet at the Heisenberg point and provide strong evidence that the isotropic model undergoes a novel finite temperature phase transition.Comment: Presented at Highly Frustrated Magnetism 2000, Waterloo, Canada. To appear in Can. J. Phy