297 research outputs found
Excited states nonlinear integral equations for an integrable anisotropic spin 1 chain
We propose a set of nonlinear integral equations to describe on the excited
states of an integrable the spin 1 chain with anisotropy. The scaling
dimensions, evaluated numerically in previous studies, are recovered
analytically by using the equations. This result may be relevant to the study
on the supersymmetric sine-Gordon model.Comment: 15 pages, 2 Figures, typos correcte
Finite temperature correlations for the U_q(sl(2|1))-invariant generalized Hubbard model
We study an integrable model of one-dimensional strongly correlated electrons
at finite temperature by explicit calculation of the correlation lengths of
various correlation functions. The model is invariant with respect to the
quantum superalgebra U_q(sl(2|1)) and characterized by the Hubbard interaction,
correlated hopping and pair-hopping terms. Using the integrability, the graded
quantum transfer matrix is constructed. From the analyticity of its
eigenvalues, a closed set of non-linear integral equations is derived which
describe the thermodynamical quantities and the finite temperature
correlations. The results show a crossover from a regime with dominating
density-density correlations to a regime with dominating superconducting pair
correlations. Analytical calculations in the low temperature limit are also
discussed.Comment: 40 pages, 19 figure
From multiple integrals to Fredholm determinants
We consider a multiple integral representation for the finite temperature
density-density correlation functions of the one-dimensional Bose gas with
delta function interaction in the limits of infinite and vanishing repulsion.
In the former case a known Fredholm determinant is recovered. In the latter
case a similar expression appears with permanents replacing determinants.Comment: 11 pages, section on the free Boson limit adde
Multi-distributed Entanglement in Finitely Correlated Chains
The entanglement-sharing properties of an infinite spin-chain are studied
when the state of the chain is a pure, translation-invariant state with a
matrix-product structure. We study the entanglement properties of such states
by means of their finitely correlated structure. These states are recursively
constructed by means of an auxiliary density matrix \rho on a matrix algebra B
and a completely positive map E: A \otimes B -> B, where A is the spin 2\times
2 matrix algebra. General structural results for the infinite chain are
therefore obtained by explicit calculations in (finite) matrix algebras. In
particular, we study not only the entanglement shared by nearest-neighbours,
but also, differently from previous works, the entanglement shared between
connected regions of the spin-chain. This range of possible applications is
illustrated and the maximal concurrence C=1/\sqrt{2} for the entanglement of
connected regions can actually be reached.Comment: 7 pages, 2 figures, to be published in Eur.Phys.Let
Thermodynamics of the Anisotropic Spin-1/2 Heisenberg Chain and Related Quantum Chains
The free energy and correlation lengths of the spin-1/2 chain are
studied at finite temperature. We use the quantum transfer matrix approach and
derive non-linear integral equations for all eigenvalues. Analytic results are
presented for the low-temperature asymptotics, in particular for the critical
chain in an external magnetic field. These results are compared to
predictions by conformal field theory. The integral equations are solved
numerically for the non-critical chain and the related spin-1 biquadratic
chain at arbitrary temperature.Comment: 31 pages, LATEX, 5 PostScript figures appended, preprint
cologne-93-471
Exact Groundstates for Antiferromagnetic Spin-One Chains with Nearest and Next-Nearest Neighbour Interactions
We have found the exact ground state for a large class of antiferromagnetic
spin-one chains with nearest and next-nearest neighbour interactions. The
ground state is characterized as a matrix product of local site states and has
the properties characteristic of the Haldane scenario.Comment: 8 pages, to appear in Z. Phys. B, preprint Cologne-94-474
Spinful bosons in an optical lattice
We analyze the behavior of cold spin-1 particles with antiferromagnetic
interactions in a one-dimensional optical lattice using density matrix
renormalization group calculations. Correlation functions and the dimerization
are shown and we also present results for the energy gap between ground state
and the spin excited states. We confirm the anticipated phase diagram, with
Mott-insulating regions of alternating dimerized S=1 chains for odd particle
density versus on-site singlets for even density. We find no evidence for any
additional ordered phases in the physically accessible region, however for
sufficiently large spin interaction, on-site singlet pairs dominate leading,
for odd density, to a breakdown of the Mott insulator or, for even density, a
real-space singlet superfluid.Comment: Minor revisions and clarification
On Matrix Product Ground States for Reaction-Diffusion Models
We discuss a new mechanism leading to a matrix product form for the
stationary state of one-dimensional stochastic models. The corresponding
algebra is quadratic and involves four different matrices. For the example of a
coagulation-decoagulation model explicit four-dimensional representations are
given and exact expressions for various physical quantities are recovered. We
also find the general structure of -point correlation functions at the phase
transition.Comment: LaTeX source, 7 pages, no figure
Thermodynamics and Crossover Phenomena in the Correlation Lengths of the One-Dimensional t-J Model
We investigate the thermodynamics of the one-dimensional t-J model using
transfer matrix renormalization group (TMRG) algorithms and present results for
quantities like particle number, specific heat, spin susceptibility and
compressibility. Based on these results we confirm a phase diagram consisting
of a Tomonaga-Luttinger liquid (TLL) phase for small J/t and a phase separated
state for J/t large. Close to phase separation we find a spin-gap
(Luther-Emery) phase at low densities consistent with predictions by other
studies. At the supersymmetric point we compare our results with exact results
from the Bethe ansatz and find excellent agreement. In particular we focus on
the calculation of correlation lengths and static correlation functions and
study the crossover from the non-universal high T lattice into the quantum
critical regime. At the supersymmetric point we compare in detail with
predictions by conformal field theory (CFT) and TLL theory and show the
importance of logarithmic corrections.Comment: 14 pages, 20 figure
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