366 research outputs found
The Onsager Algebra Symmetry of -matrices in the Superintegrable Chiral Potts Model
We demonstrate that the -matrices in the superintegrable chiral
Potts model possess the Onsager algebra symmetry for their degenerate
eigenvalues. The Fabricius-McCoy comparison of functional relations of the
eight-vertex model for roots of unity and the superintegrable chiral Potts
model has been carefully analyzed by identifying equivalent terms in the
corresponding equations, by which we extract the conjectured relation of
-operators and all fusion matrices in the eight-vertex model corresponding
to the -relation in the chiral Potts model.Comment: Latex 21 pages; Typos added, References update
Multi-particle structure in the Z_n-chiral Potts models
We calculate the lowest translationally invariant levels of the Z_3- and
Z_4-symmetrical chiral Potts quantum chains, using numerical diagonalization of
the hamiltonian for N <= 12 and N <= 10 sites, respectively, and extrapolating
N to infinity. In the high-temperature massive phase we find that the pattern
of the low-lying zero momentum levels can be explained assuming the existence
of n-1 particles carrying Z_n-charges Q = 1, ... , n-1 (mass m_Q), and their
scattering states. In the superintegrable case the masses of the n-1 particles
become proportional to their respective charges: m_Q = Q m_1. Exponential
convergence in N is observed for the single particle gaps, while power
convergence is seen for the scattering levels. We also verify that
qualitatively the same pattern appears for the self-dual and integrable cases.
For general Z_n we show that the energy-momentum relations of the particles
show a parity non-conservation asymmetry which for very high temperatures is
exclusive due to the presence of a macroscopic momentum P_m=(1-2Q/n)/\phi,
where \phi is the chiral angle and Q is the Z_n-charge of the respective
particle.Comment: 22 pages (LaTeX) plus 5 figures (included as PostScript),
BONN-HE-92-3
Eigenvectors in the Superintegrable Model I: sl_2 Generators
In order to calculate correlation functions of the chiral Potts model, one
only needs to study the eigenvectors of the superintegrable model. Here we
start this study by looking for eigenvectors of the transfer matrix of the
periodic tau_2(t)model which commutes with the chiral Potts transfer matrix. We
show that the degeneracy of the eigenspace of tau_2(t) in the Q=0 sector is
2^r, with r=(N-1)L/N when the size of the transfer matrix L is a multiple of N.
We introduce chiral Potts model operators, different from the more commonly
used generators of quantum group U-tilde_q(sl-hat(2)). From these we can form
the generators of a loop algebra L(sl(2)). For this algebra, we then use the
roots of the Drinfeld polynomial to give new explicit expressions for the
generators representing the loop algebra as the direct sum of r copies of the
simple algebra sl(2).Comment: LaTeX 2E document, 11 pages, 1 eps figure, using iopart.cls with
graphicx and iopams packages. v2: Appended text to title, added
acknowledgments and made several minor corrections v3: Added reference,
eliminated ambiguity, corrected a few misprint
On -model in Chiral Potts Model and Cyclic Representation of Quantum Group
We identify the precise relationship between the five-parameter
-family in the -state chiral Potts model and XXZ chains with
-cyclic representation. By studying the Yang-Baxter relation of the
six-vertex model, we discover an one-parameter family of -operators in terms
of the quantum group . When is odd, the -state
-model can be regarded as the XXZ chain of
cyclic representations with . The symmetry algebra of the
-model is described by the quantum affine algebra via the canonical representation. In general for an arbitrary
, we show that the XXZ chain with a -cyclic representation for
is equivalent to two copies of the same -state
-model.Comment: Latex 11 pages; Typos corrected, Minor changes for clearer
presentation, References added and updated-Journal versio
Chromosome conformation maps in fission yeast reveal cell cycle dependent sub nuclear structure
Successful progression through the cell cycle requires spatial and temporal regulation of gene transcript levels and the number, positions and condensation levels of chromosomes. Here we present a high resolution survey of genome interactions in Schizosaccharomyces pombe using synchronized cells to investigate cell cycle dependent changes in genome organization and transcription. Cell cycle dependent interactions were captured between and within S. pombe chromosomes. Known features of genome organization (e.g. the clustering of telomeres and retrotransposon long terminal repeats (LTRs)) were observed throughout the cell cycle. There were clear correlations between transcript levels and chromosomal interactions between genes, consistent with a role for interactions in transcriptional regulation at specific stages of the cell cycle. In silico reconstructions of the chromosome organization within the S. pombe nuclei were made by polymer modeling. These models suggest that groups of genes with high and low, or differentially regulated transcript levels have preferred positions within the S. pombe nucleus. We conclude that the S. pombe nucleus is spatially divided into functional sub-nuclear domains that correlate with gene activity. The observation that chromosomal interactions are maintained even when chromosomes are fully condensed in M phase implicates genome organization in epigenetic inheritance and bookmarking
Fusion Operators in the Generalized -model and Root-of-unity Symmetry of the XXZ Spin Chain of Higher Spin
We construct the fusion operators in the generalized -model using
the fused -operators, and verify the fusion relations with the truncation
identity. The algebraic Bethe ansatz discussion is conducted on two special
classes of which include the superintegrable chiral Potts model.
We then perform the parallel discussion on the XXZ spin chain at roots of
unity, and demonstrate that the -loop-algebra symmetry exists for the
root-of-unity XXZ spin chain with a higher spin, where the evaluation
parameters for the symmetry algebra are identified by the explicit
Fabricius-McCoy current for the Bethe states. Parallels are also drawn to the
comparison with the superintegrable chiral Potts model.Comment: Latex 33 Pages; Typos and errors corrected, New improved version by
adding explanations for better presentation. Terminology in the content and
the title refined. References added and updated-Journal versio
On the construction of pseudo-hermitian quantum system with a pre-determined metric in the Hilbert space
A class of pseudo-hermitian quantum system with an explicit form of the
positive-definite metric in the Hilbert space is presented. The general method
involves a realization of the basic canonical commutation relations defining
the quantum system in terms of operators those are hermitian with respect to a
pre-determined positive definite metric in the Hilbert space. Appropriate
combinations of these operators result in a large number of pseudo-hermitian
quantum systems admitting entirely real spectra and unitary time evolution. The
examples considered include simple harmonic oscillators with complex angular
frequencies, Stark(Zeeman) effect with complex electric(magnetic) field,
non-hermitian general quadratic form of N boson(fermion) operators, symmetric
and asymmetric XXZ spin-chain in complex magnetic field, non-hermitian
Haldane-Shastry spin-chain and Lipkin-Meshkov-Glick model.Comment: 29 pages, revtex, minor changes, version to appear in Journal of
Physics A(v3
The quiet crossing of ocean tipping points
Anthropogenic climate change profoundly alters the ocean’s environmental conditions, which, in turn, impact marine ecosystems. Some of these changes are happening fast and may be difficult to reverse. The identification and monitoring of such changes, which also includes tipping points, is an ongoing and emerging research effort. Prevention of negative impacts requires mitigation efforts based on feasible research-based pathways. Climate-induced tipping points are traditionally associated with singular catastrophic events (relative to natural variations) of dramatic negative impact. High-probability high-impact ocean tipping points due to warming, ocean acidification, and deoxygenation may be more fragmented both regionally and in time but add up to global dimensions. These tipping points in combination with gradual changes need to be addressed as seriously as singular catastrophic events in order to prevent the cumulative and often compounding negative societal and Earth system impacts
sl(N) Onsager's Algebra and Integrability
We define an analog of Onsager's Algebra through a finite set of
relations that generalize the Dolan Grady defining relations for the original
Onsager's Algebra. This infinite-dimensional Lie Algebra is shown to be
isomorphic to a fixed point subalgebra of Loop Algebra with respect
to a certain involution. As the consequence of the generalized Dolan Grady
relations a Hamiltonian linear in the generators of Onsager's Algebra
is shown to posses an infinite number of mutually commuting integrals of
motion
Antiperiodic dynamical 6-vertex model I: Complete spectrum by SOV, matrix elements of the identity on separate states and connections to the periodic 8-vertex model
The spin-1/2 highest weight representations of the dynamical 6-vertex and the
standard 8-vertex Yang-Baxter algebra on a finite chain are considered in this
paper. For the antiperiodic dynamical 6-vertex transfer matrix defined on
chains with an odd number of sites, we adapt the Sklyanin's quantum separation
of variable (SOV) method and explicitly construct SOV representations from the
original space of representations. We provide the complete characterization of
eigenvalues and eigenstates proving also the simplicity of its spectrum.
Moreover, we characterize the matrix elements of the identity on separated
states by determinant formulae. The matrices entering in these determinants
have elements given by sums over the SOV spectrum of the product of the
coefficients of separate states. This SOV analysis is not reduced to the case
of the elliptic roots of unit and the results here derived define the required
setup to extend to the dynamical 6-vertex model the approach recently developed
in [1]-[5] to compute the form factors of the local operators in the SOV
framework, these results will be presented in a future publication. For the
periodic 8-vertex transfer matrix, we prove that its eigenvalues have to
satisfy a fixed system of equations. In the case of a chain with an odd number
of sites, this system of equations is the same entering in the SOV
characterization of the antiperiodic dynamical 6-vertex transfer matrix
spectrum. This implies that the set of the periodic 8-vertex eigenvalues is
contained in the set of the antiperiodic dynamical 6-vertex eigenvalues. A
criterion is introduced to find simultaneous eigenvalues of these two transfer
matrices and associate to any of such eigenvalues one nonzero eigenstate of the
periodic 8-vertex transfer matrix by using the SOV results. Moreover, a
preliminary discussion on the degeneracy of the periodic 8-vertex spectrum is
also presented.Comment: 36 pages, main modifications in section 3 and one appendix added, no
result modified for the dynamical 6-vertex transfer matrix spectrum and the
matrix elements of identity on separate states for chains with an odd number
of site
- …