642 research outputs found
Thermodynamics of the 3-State Potts Spin Chain
We demonstrate the relation of the infrared anomaly of conformal field theory
with entropy considerations of finite temperature thermodynamics for the
3-state Potts chain. We compute the free energy and compute the low temperature
specific heat for both the ferromagnetic and anti-ferromagnetic spin chains,
and find the central charges for both.Comment: 18 pages, LaTex. Preprint # ITP-SB-92-60. References added and first
section expande
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
Asymmetric XXZ chain at the antiferromagnetic transition: Spectra and partition functions
The Bethe ansatz equation is solved to obtain analytically the leading
finite-size correction of the spectra of the asymmetric XXZ chain and the
accompanying isotropic 6-vertex model near the antiferromagnetic phase boundary
at zero vertical field. The energy gaps scale with size as and
its amplitudes are obtained in terms of level-dependent scaling functions.
Exactly on the phase boundary, the amplitudes are proportional to a sum of
square-root of integers and an anomaly term. By summing over all low-lying
levels, the partition functions are obtained explicitly. Similar analysis is
performed also at the phase boundary of zero horizontal field in which case the
energy gaps scale as . The partition functions for this case are found
to be that of a nonrelativistic free fermion system. From symmetry of the
lattice model under rotation, several identities between the partition
functions are found. The scaling at zero vertical field is
interpreted as a feature arising from viewing the Pokrovsky-Talapov transition
with the space and time coordinates interchanged.Comment: Minor corrections only. 18 pages in RevTex, 2 PS figure
Bethe Ansatz Equations for the Broken -Symmetric Model
We obtain the Bethe Ansatz equations for the broken -symmetric
model by constructing a functional relation of the transfer matrix of
-operators. This model is an elliptic off-critical extension of the
Fateev-Zamolodchikov model. We calculate the free energy of this model on the
basis of the string hypothesis.Comment: 43 pages, latex, 11 figure
model as effective Hamiltonian for generalized Hubbard models with broken -symmetry
We consider the limit of strong Coulomb attraction for generalized Hubbard
models with -symmetry. In this limit these models are equivalent to the
ferromagnetic spin-1/2 Heisenberg quantum spin chain. In order to study the
behaviour of the superconducting phase in the electronic model under
perturbations which break the -symmetry we investigate the ground state
of the ferromagnetic non-critical -chain in the sector with fixed
magnetization. It turns out to be a large bound state of magnons. We find
that the perturbations considered here lead to the disappearance of the
off-diagonal longe-range order.Comment: Results of previous version are generalized, new title, references
added. 10 pages, Latex, no figure
Degrees of controllability for quantum systems and applications to atomic systems
Precise definitions for different degrees of controllability for quantum
systems are given, and necessary and sufficient conditions are discussed. The
results are applied to determine the degree of controllability for various
atomic systems with degenerate energy levels and transition frequencies.Comment: 20 pages, IoP LaTeX, revised and expanded versio
Impact of positivity and complete positivity on accessibility of Markovian dynamics
We consider a two-dimensional quantum control system evolving under an
entropy-increasing irreversible dynamics in the semigroup form. Considering a
phenomenological approach to the dynamics, we show that the accessibility
property of the system depends on whether its evolution is assumed to be
positive or completely positive. In particular, we characterize the family of
maps having different accessibility and show the impact of that property on
observable quantities by means of a simple physical model.Comment: 11 pages, to appear in J. Phys.
Spin operator matrix elements in the superintegrable chiral Potts quantum chain
We derive spin operator matrix elements between general eigenstates of the
superintegrable Z_N-symmetric chiral Potts quantum chain of finite length. Our
starting point is the extended Onsager algebra recently proposed by R.Baxter.
For each pair of spaces (Onsager sectors) of the irreducible representations of
the Onsager algebra, we calculate the spin matrix elements between the
eigenstates of the Hamiltonian of the quantum chain in factorized form, up to
an overall scalar factor. This factor is known for the ground state Onsager
sectors. For the matrix elements between the ground states of these sectors we
perform the thermodynamic limit and obtain the formula for the order
parameters. For the Ising quantum chain in a transverse field (N=2 case) the
factorized form for the matrix elements coincides with the corresponding
expressions obtained recently by the Separation of Variables Method.Comment: 24 pages, 1 figur
The structure of quotients of the Onsager algebra by closed ideals
We study the Onsager algebra from the ideal theoretic point of view. A
complete classification of closed ideals and the structure of quotient algebras
are obtained. We also discuss the solvable algebra aspect of the Onsager
algebra through the use of formal Lie algebras.Comment: 33 pages, Latex, small topos corrected-Journal versio
The Blob Algebra and the Periodic Temperley-Lieb Algebra
We determine the structure of two variations on the Temperley-Lieb algebra,
both used for dealing with special kinds of boundary conditions in statistical
mechanics models.
The first is a new algebra, the `blob' algebra (the reason for the name will
become obvious shortly!). We determine both the generic and all the exceptional
structures for this two parameter algebra. The second is the periodic
Temperley-Lieb algebra. The generic structure and part of the exceptional
structure of this algebra have already been studied. Here we complete the
analysis, using results from the study of the blob algebra.Comment: 12 page
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