1,296 research outputs found
Exactly solvable quantum spin ladders associated with the orthogonal and symplectic Lie algebras
We extend the results of spin ladder models associated with the Lie algebras
to the case of the orthogonal and symplectic algebras $o(2^n),\
sp(2^n)$ where n is the number of legs for the system. Two classes of models
are found whose symmetry, either orthogonal or symplectic, has an explicit n
dependence. Integrability of these models is shown for an arbitrary coupling of
XX type rung interactions and applied magnetic field term.Comment: 7 pages, Late
Raise and Peel Models of fluctuating interfaces and combinatorics of Pascal's hexagon
The raise and peel model of a one-dimensional fluctuating interface (model A)
is extended by considering one source (model B) or two sources (model C) at the
boundaries. The Hamiltonians describing the three processes have, in the
thermodynamic limit, spectra given by conformal field theory. The probability
of the different configurations in the stationary states of the three models
are not only related but have interesting combinatorial properties. We show
that by extending Pascal's triangle (which gives solutions to linear relations
in terms of integer numbers), to an hexagon, one obtains integer solutions of
bilinear relations. These solutions give not only the weights of the various
configurations in the three models but also give an insight to the connections
between the probability distributions in the stationary states of the three
models. Interestingly enough, Pascal's hexagon also gives solutions to a
Hirota's difference equation.Comment: 33 pages, an abstract and an introduction are rewritten, few
references are adde
Magnetization Plateaux in Bethe Ansatz Solvable Spin-S Ladders
We examine the properties of the Bethe Ansatz solvable two- and three-leg
spin- ladders. These models include Heisenberg rung interactions of
arbitrary strength and thus capture the physics of the spin- Heisenberg
ladders for strong rung coupling. The discrete values derived for the
magnetization plateaux are seen to fit with the general prediction based on the
Lieb-Schultz- Mattis theorem. We examine the magnetic phase diagram of the
spin-1 ladder in detail and find an extended magnetization plateau at the
fractional value in agreement with the experimental observation
for the spin-1 ladder compound BIP-TENO.Comment: 11 pages, 1 figur
Relaxation rate of the reverse biased asymmetric exclusion process
We compute the exact relaxation rate of the partially asymmetric exclusion
process with open boundaries, with boundary rates opposing the preferred
direction of flow in the bulk. This reverse bias introduces a length scale in
the system, at which we find a crossover between exponential and algebraic
relaxation on the coexistence line. Our results follow from a careful analysis
of the Bethe ansatz root structure.Comment: 22 pages, 12 figure
Slowest relaxation mode of the partially asymmetric exclusion process with open boundaries
We analyze the Bethe ansatz equations describing the complete spectrum of the
transition matrix of the partially asymmetric exclusion process on a finite
lattice and with the most general open boundary conditions. We extend results
obtained recently for totally asymmetric diffusion [J. de Gier and F.H.L.
Essler, J. Stat. Mech. P12011 (2006)] to the case of partial symmetry. We
determine the finite-size scaling of the spectral gap, which characterizes the
approach to stationarity at large times, in the low and high density regimes
and on the coexistence line. We observe boundary induced crossovers and discuss
possible interpretations of our results in terms of effective domain wall
theories.Comment: 30 pages, 9 figures, typeset for pdflatex; revised versio
Exact expressions for correlations in the ground state of the dense O(1) loop model
Conjectures for analytical expressions for correlations in the dense O
loop model on semi infinite square lattices are given. We have obtained these
results for four types of boundary conditions. Periodic and reflecting boundary
conditions have been considered before. We give many new conjectures for these
two cases and review some of the existing results. We also consider boundaries
on which loops can end. We call such boundaries ''open''. We have obtained
expressions for correlations when both boundaries are open, and one is open and
the other one is reflecting. Also, we formulate a conjecture relating the
ground state of the model with open boundaries to Fully Packed Loop models on a
finite square grid. We also review earlier obtained results about this relation
for the three other types of boundary conditions. Finally, we construct a
mapping between the ground state of the dense O loop model and the XXZ
spin chain for the different types of boundary conditions.Comment: 25 pages, version accepted by JSTA
Exact Spectral Gaps of the Asymmetric Exclusion Process with Open Boundaries
We derive the Bethe ansatz equations describing the complete spectrum of the
transition matrix of the partially asymmetric exclusion process with the most
general open boundary conditions. By analysing these equations in detail for
the cases of totally asymmetric and symmetric diffusion, we calculate the
finite-size scaling of the spectral gap, which characterizes the approach to
stationarity at large times. In the totally asymmetric case we observe boundary
induced crossovers between massive, diffusive and KPZ scaling regimes. We
further study higher excitations, and demonstrate the absence of oscillatory
behaviour at large times on the ``coexistence line'', which separates the
massive low and high density phases. In the maximum current phase, oscillations
are present on the KPZ scale . While independent of the
boundary parameters, the spectral gap as well as the oscillation frequency in
the maximum current phase have different values compared to the totally
asymmetric exclusion process with periodic boundary conditions. We discuss a
possible interpretation of our results in terms of an effective domain wall
theory.Comment: 42 pages, 25 figures; added appendix and minor correction
Refined Razumov-Stroganov conjectures for open boundaries
Recently it has been conjectured that the ground-state of a Markovian
Hamiltonian, with one boundary operator, acting in a link pattern space is
related to vertically and horizontally symmetric alternating-sign matrices
(equivalently fully-packed loop configurations (FPL) on a grid with special
boundaries).We extend this conjecture by introducing an arbitrary boundary
parameter. We show that the parameter dependent ground state is related to
refined vertically symmetric alternating-sign matrices i.e. with prescribed
configurations (respectively, prescribed FPL configurations) in the next to
central row.
We also conjecture a relation between the ground-state of a Markovian
Hamiltonian with two boundary operators and arbitrary coefficients and some
doubly refined (dependence on two parameters) FPL configurations. Our
conjectures might be useful in the study of ground-states of the O(1) and XXZ
models, as well as the stationary states of Raise and Peel models.Comment: 11 pages LaTeX, 8 postscript figure
Magnetic Susceptibility of an integrable anisotropic spin ladder system
We investigate the thermodynamics of a spin ladder model which possesses a
free parameter besides the rung and leg couplings. The model is exactly solved
by the Bethe Ansatz and exhibits a phase transition between a gapped and a
gapless spin excitation spectrum. The magnetic susceptibility is obtained
numerically and its dependence on the anisotropy parameter is determined. A
connection with the compounds KCuCl3, Cu2(C5H12N2)2Cl4 and (C5H12N)2CuBr4 in
the strong coupling regime is made and our results for the magnetic
susceptibility fit the experimental data remarkably well.Comment: 12 pages, 12 figures included, submitted to Phys. Rev.
Phase diagram of the su(8) quantum spin tube
We calculate the phase diagram of an integrable anisotropic 3-leg quantum
spin tube connected to the su(8) algebra. We find several quantum phase
transitions for antiferromagnetic rung couplings. Their locations are
calculated exactly from the Bethe Ansatz solution and we discuss the nature of
each of the different phases.Comment: 10 pages, RevTeX, 1 postscript figur
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