87 research outputs found
Wither the sliding Luttinger liquid phase in the planar pyrochlore
Using series expansion based on the flow equation method we study the zero
temperature properties of the spin-1/2 planar pyrochlore antiferromagnet in the
limit of strong diagonal coupling. Starting from the limit of decoupled crossed
dimers we analyze the evolution of the ground state energy and the elementary
triplet excitations in terms of two coupling constants describing the inter
dimer exchange. In the limit of weakly coupled spin-1/2 chains we find that the
fully frustrated inter chain coupling is critical, forcing a dimer phase which
adiabatically connects to the state of isolated dimers. This result is
consistent with findings by O. Starykh, A. Furusaki and L. Balents (Phys. Rev.
B 72, 094416 (2005)) which is inconsistent with a two-dimensional sliding
Luttinger liquid phase at finite inter chain coupling.Comment: 6 pages, 4 Postscript figures, 1 tabl
Ab initio computation of d-d excitation energies in low-dimensional Ti and V oxychlorides
Using a quantum chemical cluster-in-solid computational scheme, we calculate
the local d-d excitation energies for two strongly correlated Mott insulators,
the oxychlorides TiOCl and VOCl. TiOCl harbors quasi-one-dimensional spin
chains made out of S = 1/2 Ti3+ ions while the electronic structure of VOCl
displays a more two-dimensional character. We find in both cases that the
lowest-energy d-d excitations are within the t2g subshell, starting at 0.34 eV
and indicating that orbital degeneracies are significantly lifted. In the
vanadium oxychloride, spin triplet to singlet excitations are calculated to be
1 eV higher in energy. For TiOCl, the computed d-level electronic structure and
the symmetries of the wavefunctions are in very good agreement with resonant
inelastic x-ray scattering results and optical absorption data. For VOCl,
future resonant inelastic x-ray scattering experiments will constitute a direct
test of the symmetry and energy of about a dozen of different d-d excitations
that we predict here
On the thermodynamic limit of form factors in the massless XXZ Heisenberg chain
We consider the problem of computing form factors of the massless XXZ
Heisenberg spin-1/2 chain in a magnetic field in the (thermodynamic) limit
where the size M of the chain becomes large. For that purpose, we take the
particular example of the matrix element of the third component of spin between
the ground state and an excited state with one particle and one hole located at
the opposite ends of the Fermi interval (umklapp-type term). We exhibit its
power-law decrease in terms of the size of the chain M, and compute the
corresponding exponent and amplitude. As a consequence, we show that this form
factor is directly related to the amplitude of the leading oscillating term in
the long-distance asymptotic expansion of the two-point correlation function of
the third component of spin.Comment: 28 page
Discrete element modelling of rock communition in a cone crusher using a bonded particle model
It is known that discrete element method modelling (DEM) of rock size reduction can be achieved by two approaches: the population balance model (PBM) and the bonded particle model (BPM). However, only PBM has been successfully used in DEM modelling cone crusher in the literature. The aim of this paper is to explore the feasibility of using the BPM to represent the size reduction of rock experienced within the cone crusher chamber. The feed rock particles were represented by isotropic dense random packing agglomerates. The simulation results were compared with the PBM simulation results, and it was shown that the BPM cone crusher model was able to satisfactorily replicate the performance of a cone crusher as well and it can provide more accurate prediction of the percentage of the fine products. In addition, the novel contribution here is that the rock feed material comprises particles of realistic shapes which break into more realistically shaped fragments compared with the fragments with defined shapes in the PBM model
Form factors and complete spectrum of XXX antiperiodic higher spin chains by quantum separation of variables
The antiperiodic transfer matrix associated to higher spin representations of
the rational 6-vertex Yang-Baxter algebra is analyzed by generalizing the
approach introduced recently in [1], for the cyclic representations, in [2],
for the spin-1/2 highest weight representations, and in [3], for the spin 1/2
representations of the reflection algebra. Here, we derive the complete
characterization of the transfer matrix spectrum and we prove its simplicity in
the framework of Sklyanin's quantum separation of variables (SOV). Then, the
characterization of local operators by Sklyanin's quantum separate variables
and the expression of the scalar products of separates states by determinant
formulae allow to compute the form factors of the local spin operators by one
determinant formulae similar to the scalar product ones. Finally, let us
comment that these results represent the SOV analogous in the antiperiodic
higher spin XXX quantum chains of the results obtained for the periodic chains
in [4] in the framework of the algebraic Bethe ansatz.Comment: 20 pages, introduction improved by taking into account some relevant
references on the spectrum of the model under general boundary conditions, no
further relevant modification
DMRG study of scaling exponents in spin-1/2 Heisenberg chains with dimerization and frustration
In conformal field theory, key properties of spin-1/2 chains, such as the
ground state energy per site and the excitation gap scale with dimerization
delta as delta^alpha with known exponents alpha and logarithmic corrections.
The logarithmic corrections vanish in a spin chain with nearest (J=1) and next
nearest neighbor interactions (J_2), for J_2c=0.2411. DMRG analysis of a
frustrated spin chain with no logarithmic corrections yields the field
theoretic values of alpha, and the scaling relation is valid up to the
physically realized range, delta ~ 0.1. However, chains with logarithmic
corrections (J_2<0.2411 J) are more accurately fit by simple power laws with
different exponents for physically realized dimerizations. We show the
exponents decreasing from approximately 3/4 to 2/3 for the spin gap and from
approximately 3/2 to 4/3 for the energy per site and error bars in the exponent
also decrease as J_2 approaches to J_2c.Comment: 9 pages including two figures; added standard deviations of various
fitting parameters such as exponents, and several references to earlier wor
Three-leg Antiferromagnetic Heisenberg Ladder with Frustrated Boundary Condition; Ground State Properties
The antiferromagnetic Heisenberg spin systems on the three-leg ladder are
investigated. Periodic boundary condition is imposed in the rung direction. The
system has an excitation gap for all antiferromagnetic inter-chain coupling
(). The estimated gap for the strong coupling limit
() is 0.28. Although the interaction is
homogeneous and only nearest-neighbor, the ground states of the system are
dimerized and break the translational symmetry in the thermodynamic limit.
Introducing the next-nearest neighbor coupling (), we can see that the
system is solved exactly. The ground state wave function is completely
dimer-ordered. Using density matrix renomalization group algorithm, we show
numerically that the original model () has the same nature with the
exactly solvable model. The ground state properties of the ladder with a higher
odd number of legs are also discussed.Comment: 15 pages, LaTeX, to be published in J.Phys.Soc.Jpn. Vol. 66 No. 1
Generalized Valence Bond State and Solvable Models for Spin-1/2 Systems with Orbital degeneracy
A spin-1/2 system with double orbital degeneracy may possess SU(4) symmetry.
According to the group theory a global SU(4) singelt state can be expressed as
a linear combination of all possible configurations consisting of four-site
SU(4) singlets. Following P. W. Andersion's idea for spin 1/2 system, we
propose that the ground state for the antiferromagnetic SU(4) model is SU(4)
resonating valence bond (RVB) state. A short-range SU(4) RVB state is a spin
and orbital liquid, and its elementary excitations has an energy gap. We
construct a series of solvale models which ground states are short-range SU(4)
RVB states. The results can be generalized to the antiferromagnetic SU(N)
models.Comment: 4 page
Valence Bond States: Link models
An isotropic anti-ferromagnetic quantum state on a square lattice is
characterized by symmetry arguments only. By construction, this quantum state
is the result of an underlying valence bond structure without breaking any
symmetry in the lattice or spin spaces. A detailed analysis of the correlations
of the quantum state is given (using a mapping to a 2D classical statistical
model and methods in field theory like mapping to the non-linear sigma model or
bosonization techniques) as well as the results of numerical treatments
(regarding exact diagonalization and variational methods). Finally, the
physical relevance of the model is motivated. A comparison of the model to
known anti-ferromagnetic Mott-Hubbard insulators is given by means of the
two-point equal-time correlation function obtained i) numerically from the
suggested state and ii) experimentally from neutron scattering on cuprates in
the anti-ferromagnetic insulator phase.Comment: 20 pages, 15 figures; added references, corrected some typos, new
sections. Published versio
Quasi-normal frequencies: Key analytic results
The study of exact quasi-normal modes [QNMs], and their associated
quasi-normal frequencies [QNFs], has had a long and convoluted history -
replete with many rediscoveries of previously known results. In this article we
shall collect and survey a number of known analytic results, and develop
several new analytic results - specifically we shall provide several new QNF
results and estimates, in a form amenable for comparison with the extant
literature. Apart from their intrinsic interest, these exact and approximate
results serve as a backdrop and a consistency check on ongoing efforts to find
general model-independent estimates for QNFs, and general model-independent
bounds on transmission probabilities. Our calculations also provide yet another
physics application of the Lambert W function. These ideas have relevance to
fields as diverse as black hole physics, (where they are related to the damped
oscillations of astrophysical black holes, to greybody factors for the Hawking
radiation, and to more speculative state-counting models for the Bekenstein
entropy), to quantum field theory (where they are related to Casimir energies
in unbounded systems), through to condensed matter physics, (where one may
literally be interested in an electron tunelling through a physical barrier).Comment: V1: 29 pages; V2: Reformatted, 31 pages. Title changed to reflect
major additions and revisions. Now describes exact QNFs for the double-delta
potential in terms of the Lambert W function. V3: Minor edits for clarity.
Four references added. No physics changes. Still 31 page
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