124 research outputs found
The nested SU(N) off-shell Bethe ansatz and exact form factors
The form factor equations are solved for an SU(N) invariant S-matrix under
the assumption that the anti-particle is identified with the bound state of N-1
particles. The solution is obtained explicitly in terms of the nested off-shell
Bethe ansatz where the contribution from each level is written in terms of
multiple contour integrals.Comment: This work is dedicated to the 75th anniversary of H. Bethe's
foundational work on the Heisenberg chai
Towards the Construction of Wightman Functions of Integrable Quantum Field Theories
The purpose of the ``bootstrap program'' for integrable quantum field
theories in 1+1 dimensions is to construct a model in terms of its Wightman
functions explicitly. In this article, this program is mainly illustrated in
terms of the sine-Gordon and the sinh-Gordon model and (as an exercise) the
scaling Ising model. We review some previous results on sine-Gordon breather
form factors and quantum operator equations. The problem to sum over
intermediate states is attacked in the short distance limit of the two point
Wightman function for the sinh-Gordon and the scaling Ising model.Comment: LATEX 18 pages, Talk presented at the '6th International Workshop on
Conformal Field Theories and Integrable Models', in Chernologka, September
200
Resolution of the Nested Hierarchy for Rational sl(n) Models
We construct Drinfel'd twists for the rational sl(n) XXX-model giving rise to
a completely symmetric representation of the monodromy matrix. We obtain a
polarization free representation of the pseudoparticle creation operators
figuring in the construction of the Bethe vectors within the framework of the
quantum inverse scattering method. This representation enables us to resolve
the hierarchy of the nested Bethe ansatz for the sl(n) invariant rational
Heisenberg model. Our results generalize the findings of Maillet and Sanchez de
Santos for sl(2) models.Comment: 25 pages, no figure
Matrix difference equations for the supersymmetric Lie algebra sl(2,1) and the `off-shell' Bethe ansatz
Based on the rational R-matrix of the supersymmetric sl(2,1) matrix
difference equations are solved by means of a generalization of the nested
algebraic Bethe ansatz. These solutions are shown to be of highest-weight with
respect to the underlying graded Lie algebra structure.Comment: 10 pages, LaTex, references and acknowledgements added, spl(2,1) now
called sl(2,1
Loop algorithm for Heisenberg models with biquadratic interaction and phase transitions in two dimensions
We present a new algorithm for quantum Monte Carlo simulation based on global
updating with loops. While various theoretical predictions are confirmed in one
dimension, we find, for S=1 systems on a square lattice with an
antiferromagnetic biquadratic interaction, that the intermediate phase between
the antiferromagnetic and the ferromagnetic phases is disordered and that the
two phase transitions are both of the first order in contrast to the
one-dimensional case. It is strongly suggested that the transition points
coincide those at which the algorithm changes qualitatively.Comment: 4 pages including 4 figures, to appear in JPS
Algebraic Bethe Ansatz for a discrete-state BCS pairing model
We show in detail how Richardson's exact solution of a discrete-state BCS
(DBCS) model can be recovered as a special case of an algebraic Bethe Ansatz
solution of the inhomogeneous XXX vertex model with twisted boundary
conditions: by implementing the twist using Sklyanin's K-matrix construction
and taking the quasiclassical limit, one obtains a complete set of conserved
quantities, H_i, from which the DBCS Hamiltonian can be constructed as a second
order polynomial. The eigenvalues and eigenstates of the H_i (which reduce to
the Gaudin Hamiltonians in the limit of infinitely strong coupling) are exactly
known in terms of a set of parameters determined by a set of on-shell Bethe
Ansatz equations, which reproduce Richardson's equations for these parameters.
We thus clarify that the integrability of the DBCS model is a special case of
the integrability of the twisted inhomogeneous XXX vertex model. Furthermore,
by considering the twisted inhomogeneous XXZ model and/or choosing a generic
polynomial of the H_i as Hamiltonian, more general exactly solvable models can
be constructed. -- To make the paper accessible to readers that are not Bethe
Ansatz experts, the introductory sections include a self-contained review of
those of its feature which are needed here.Comment: 17 pages, 5 figures, submitted to Phys. Rev.
Probable absence of a quadrupolar spin-nematic phase in the bilinear-biquadratic spin-1 chain
We study numerically the ground-state phase diagram of the
bilinear-biquadratic spin-1 chain near the ferromagnetic instability point,
where the existence of a gapped or gapless nondimerized quantum nematic phase
has been suggested. Our results, obtained by a highly accurate density-matrix
renormalization-group (DMRG) calculation are consistent with the view that the
order parameter characterizing the dimer phase vanishes only at the point where
the system becomes ferromagnetic, although the existence of a gapped or gapless
nondimerized phase in a very narrow parameter range between the ferromagnetic
and the dimerized regimes cannot be ruled out.Comment: 6 pages, 6 figure
Integrable versus Non-Integrable Spin Chain Impurity Models
Recent renormalization group studies of impurities in spin-1/2 chains appear
to be inconsistent with Bethe ansatz results for a special integrable model. We
study this system in more detail around the integrable point in parameter space
and argue that this integrable impurity model corresponds to a non-generic
multi-critical point. Using previous results on impurities in half-integer spin
chains, a consistent renormalization group flow and phase diagram is proposed.Comment: 20 pages 11 figures obtainable from authors, REVTEX 3.
Exact Asymptotic Behaviour of Fermion Correlation Functions in the Massive Thirring Model
We obtain an exact asymptotic expression for the two-point fermion
correlation functions in the massive Thirring model (MTM) and show that, for
, they reproduce the exactly known corresponding functions of the
massless theory, explicitly confirming the irrelevance of the mass term at this
point. This result is obtained by using the Coulomb gas representation of the
fermionic MTM correlators in the bipolar coordinate system.Comment: To appear in J. Phys. A: Math. Gen. 12 page
Implementation of Spin Hamiltonians in Optical Lattices
We propose an optical lattice setup to investigate spin chains and ladders.
Electric and magnetic fields allow us to vary at will the coupling constants,
producing a variety of quantum phases including the Haldane phase, critical
phases, quantum dimers etc. Numerical simulations are presented showing how
ground states can be prepared adiabatically. We also propose ways to measure a
number of observables, like energy gap, staggered magnetization, end-chain
spins effects, spin correlations and the string order parameter
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