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 $\beta^2=8\pi$, 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