arXiv subjects
Publications and source records attributed to Giuseppe Albertini.
A two-parameter family of quantum spin ladders with local bilinear and biquadratic interactions is shown to be solvable by a mapping onto fragments of integrable spin 1 chains. The phase diagram, consisting of four phases, and the ground state properties are discussed. In one novel phase, the ground state is made up of plaquette singlets and rung singlets, alternating with a three-rung periodicity.
It is shown that the sl(2)q-invariant open antiferromagnetic XXZ spin chain with a boundary field has a gapless sector in the thermodynamic limit when its length is odd. Owing to a Temperley-Lieb equivalence of the spectra, the same conclusion is drawn for the purely biquadratic spin 1 chain with open boundaries and odd length.
The transition from the ordered commensurate phase to the incommensurate gaussian phase of the antiferroelectric asymmetric six-vertex model is investigated by keeping the temperature constant below the roughening point and varying the external fields $(h,v)$. In the $(h,v)$ plane, the phase boundary is approached along straight lines $δv=k δh$, where $(δh,δv)$ measures the displacement from the phase boundary. It is found that the free energy singularity displays the exponent 3/2 typical of the Pokrovski-Talapov transition $δf \sim const (δh)^{3/2}$ for any direction other than the tangential one. In the latter case $δf$ shows a discontinuity in the third derivative.
We consider the asymmetric six--vertex model, {\it i.e.} the symmetric six--vertex model in an external field with both horizontal and vertical components, and the relevant asymmetric $XXZ$ chain. The model is widely used to describe the equilibrium shape of a crystal. By means of the Bethe Ansatz solution we determine the exact free energy singularity, as function of both components of the field, at two special points on the phase boundary. We confirm the exponent $\frac{3}{2}$ (already checked experimentally), as the antiferroelectric ordered phase is reached from the incommensurate phase normally to the phase boundary, and we determine a new singularity along the tangential direction. Both singularities describe the rounding off of the crystal near a facet. The hole excitations of the spin chain at this point on the phase boundary show dispersion relations with the striking form $ΔE\sim (ΔP)^{\half}$ at small momenta, leading to a finite size scaling $ΔE \sim N^{-\half}$ for the low--lying excited states, where $N$ is the size of the chain. We conjecture that a Pokrovskii--Talapov phase transition is replaced at this point by a transition with diverging correlation length, but not classified in terms of conformal field theory.
The low-lying excitations of the asymmetric $XXZ$ spin chain are derived explicitly in the antiferromagnetic regime through the Bethe Ansatz. It is found that a massless and conformal invariant phase with central charge $c=1$ is separated from a massive phase by a line on which the low-lying excitations surprisingly scale with the lattice length as $ΔE \sim N^{-\frac{1}{2}}$. The mass gap vanishes with an exponent $\frac{1}{2}$ as one approaches the massless phase. The connection with the asymmetric $6$--vertex model and some physical consequences are discussed.
The sector of zero $Z_{N}$-charge is studied for the ferromagnetic (FM) and antiferromagnetic (AFM) version of the $Z_{N}\times Z_{2}$ invariant Fateev-Zamolodchikov quantum spin chain. We conjecture that the relevant Bethe ansatz equations should admit, beside the usual string-like solutions, exceptional multiplets, and a number of non-physical solutions. Once the physical ones are identified, we show how to get completeness and the gapless excitation spectrum. The central charge is computed from the specific heat and found to be $c=2\frac{N-1}{N+2}$ (FM) and $c=1$ (AFM).