432 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
Bethe Equation of -model and Eigenvalues of Finite-size Transfer Matrix of Chiral Potts Model with Alternating Rapidities
We establish the Bethe equation of the -model in the -state
chiral Potts model (including the degenerate selfdual cases) with alternating
vertical rapidities. The eigenvalues of a finite-size transfer matrix of the
chiral Potts model are computed by use of functional relations. The
significance of the "alternating superintegrable" case of the chiral Potts
model is discussed, and the degeneracy of -model found as in the
homogeneous superintegrable chiral Potts model.Comment: Latex 25 pages; Typos corrected, Minor changes for clearer
presentation, References added-Journal versio
Factorized finite-size Ising model spin matrix elements from Separation of Variables
Using the Sklyanin-Kharchev-Lebedev method of Separation of Variables adapted
to the cyclic Baxter--Bazhanov--Stroganov or -model, we derive
factorized formulae for general finite-size Ising model spin matrix elements,
proving a recent conjecture by Bugrij and Lisovyy
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
The tau_2-model and the chiral Potts model revisited: completeness of Bethe equations from Sklyanin's SOV method
The most general cyclic representations of the quantum integrable tau_2-model
are analyzed. The complete characterization of the tau_2-spectrum (eigenvalues
and eigenstates) is achieved in the framework of Sklyanin's Separation of
Variables (SOV) method by extending and adapting the ideas first introduced in
[1, 2]: i) The determination of the tau_2-spectrum is reduced to the
classification of the solutions of a given functional equation in a class of
polynomials. ii) The determination of the tau_2-eigenstates is reduced to the
classification of the solutions of an associated Baxter equation. These last
solutions are proven to be polynomials for a quite general class of
tau_2-self-adjoint representations and the completeness of the associated Bethe
ansatz type equations is derived. Finally, the following results are derived
for the inhomogeneous chiral Potts model: i) Simplicity of the spectrum, for
general representations. ii) Complete characterization of the chiral Potts
spectrum (eigenvalues and eigenstates) and completeness of Bethe ansatz type
equations, for the self-adjoint representations of tau_2-model on the chiral
Potts algebraic curves.Comment: 40 pages. Minor modifications in the text and some notation
Magnetic Dipole Sum Rules for Odd-Mass Nuclei
Sum rules for the total- and scissors-mode M1 strength in odd-A nuclei are
derived within the single-j interacting boson-fermion model. We discuss the
physical content and geometric interpretation of these sum rules and apply them
to ^{167}Er and ^{161}Dy. We find consistency with the former measurements but
not with the latter.Comment: 13 pages, Revtex, 1 figure, Phys. Rev. Lett. in pres
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
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
Does working memory training have to be adaptive?
This study tested the common assumption that, to be most effective, working memory (WM) training should be adaptive (i.e., task difficulty is adjusted to individual performance). Indirect evidence for this assumption stems from studies comparing adaptive training to a condition in which tasks are practiced on the easiest level of difficulty only [cf. Klingberg (Trends Cogn Sci 14:317-324, 2010)], thereby, however, confounding adaptivity and exposure to varying task difficulty. For a more direct test of this hypothesis, we randomly assigned 130 young adults to one of the three WM training procedures (adaptive, randomized, or self-selected change in training task difficulty) or to an active control group. Despite large performance increases in the trained WM tasks, we observed neither transfer to untrained structurally dissimilar WM tasks nor far transfer to reasoning. Surprisingly, neither training nor transfer effects were modulated by training procedure, indicating that exposure to varying levels of task difficulty is sufficient for inducing training gains
Quivers, YBE and 3-manifolds
We study 4d superconformal indices for a large class of N=1 superconformal
quiver gauge theories realized combinatorially as a bipartite graph or a set of
"zig-zag paths" on a two-dimensional torus T^2. An exchange of loops, which we
call a "double Yang-Baxter move", gives the Seiberg duality of the gauge
theory, and the invariance of the index under the duality is translated into
the Yang-Baxter-type equation of a spin system defined on a "Z-invariant"
lattice on T^2. When we compactify the gauge theory to 3d, Higgs the theory and
then compactify further to 2d, the superconformal index reduces to an integral
of quantum/classical dilogarithm functions. The saddle point of this integral
unexpectedly reproduces the hyperbolic volume of a hyperbolic 3-manifold. The
3-manifold is obtained by gluing hyperbolic ideal polyhedra in H^3, each of
which could be thought of as a 3d lift of the faces of the 2d bipartite
graph.The same quantity is also related with the thermodynamic limit of the BPS
partition function, or equivalently the genus 0 topological string partition
function, on a toric Calabi-Yau manifold dual to quiver gauge theories. We also
comment on brane realization of our theories. This paper is a companion to
another paper summarizing the results.Comment: 61 pages, 16 figures; v2: typos correcte
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