45,086 research outputs found
The spectrum of a vertex model and related spin one chain sitting in a genus five curve
We derive the transfer matrix eigenvalues of a three-state vertex model whose
weights are based on a -matrix not of difference form with spectral
parameters lying on a genus five curve. We have shown that the basic building
blocks for both the transfer matrix eigenvalues and Bethe equations can be
expressed in terms of meromorphic functions on an elliptic curve. We discuss
the properties of an underlying spin one chain originated from a particular
choice of the -matrix second spectral parameter. We present
numerical and analytical evidences that the respective low-energy excitations
can be gapped or massless depending on the strength of the interaction
coupling. In the massive phase we provide analytical and numerical evidences in
favor of an exact expression for the lowest energy gap. We point out that the
critical point separating these two distinct physical regimes coincides with
the one in which the weights geometry degenerate into union of genus one
curves.Comment: 22 pages, 12 figure
Integrable Vertex Models with General Twists
We review recent progress towards the solution of exactly solved isotropic
vertex models with arbitrary toroidal boundary conditions. Quantum space
transformations make it possible the diagonalization of the corresponding
transfer matrices by means of the quantum inverse scattering method. Explicit
expressions for the eigenvalues and Bethe ansatz equations of the twisted
isotropic spin chains based on the , and Lie algebras are
presented. The applicability of this approach to the eight vertex model with
non-diagonal twists is also discussed.Comment: 9 pages, Proceedings of Recent Progress in Solvable Models: RIMS
Project, Kyoto, Japan, 20-23 July 200
Algebraic Geometry methods associated to the one-dimensional Hubbard model
In this paper we study the covering vertex model of the one-dimensional
Hubbard Hamiltonian constructed by Shastry in the realm of algebraic geometry.
We show that the Lax operator sits in a genus one curve which is not isomorphic
but only isogenous to the curve suitable for the AdS/CFT context. We provide an
uniformization of the Lax operator in terms of ratios of theta functions
allowing us to establish relativistic like properties such as crossing and
unitarity. We show that the respective -matrix weights lie on an
Abelian surface being birational to the product of two elliptic curves with
distinct -invariants. One of the curves is isomorphic to that of
the Lax operator but the other is solely fourfold isogenous. These results
clarify the reason the -matrix can not be written using only
difference of spectral parameters of the Lax operator.Comment: 24 page
Mind-life continuity: a qualitative study of conscious experience
There are two fundamental models to understanding the phenomenon of natural life. One is thecomputational model, which is based on the symbolic thinking paradigm. The other is the biologicalorganism model. The common difficulty attributed to these paradigms is that their reductive tools allowthe phenomenological aspects of experience to remain hidden behind yes/no responses (behavioraltests), or brain ‘pictures’ (neuroimaging). Hence, one of the problems regards how to overcome meth-odological difficulties towards a non-reductive investigation of conscious experience. It is our aim in thispaper to show how cooperation between Eastern and Western traditions may shed light for a non-reductive study of mind and life. This study focuses on the first-person experience associated withcognitive and mental events. We studied phenomenal data as a crucial fact for the domain of livingbeings, which, we expect, can provide the ground for a subsequent third-person study. The interventionwith Jhana meditation, and its qualitative assessment, provided us with experiential profiles based uponsubjects' evaluations of their own conscious experiences. The overall results should move towards anintegrated or global perspective on mind where neither experience nor external mechanisms have thefinal wor
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