Connecting lattice and relativistic models via conformal field theory

We consider the quantum group invariant XXZ-model. In infrared limit it describes Conformal Field Theory with modified energy-momentum tensor. The correlation functions are related to solutions of level -4 of qKZ equations. We describe these solutions relating them to level 0 solutions. We further consider general matrix elements (form factors) containing local operators and asymptotic states. We explain that the formulae for solutions of qKZ equations suggest a decomposition of these matrix elements with respect to states of corresponding Conformal Field Theory .Comment: 22 pages, 1 figur

Integral representations for correlation functions of the XXZ chain at finite temperature

We derive a novel multiple integral representation for a generating function of the \s^z-\s^z correlation functions of the spin-\2 XXZ chain at finite temperature and finite, longitudinal magnetic field. Our work combines algebraic Bethe ansatz techniques for the calculation of matrix elements with the quantum transfer matrix approach to thermodynamics.Comment: 33 pages, 2 figures, v2: 2 typos corrected, 1 figure adde

Thermodynamics and short-range correlations of the XXZ chain close to its triple point

The XXZ quantum spin chain has a triple point in its ground state $h$-$1/\Delta$ phase diagram. This first order critical point is located at the joint end point of the two second order phase transition lines marking the transition from the gapless phase to the fully polarized phase and to the N\'eel ordered phase, respectively. We explore the magnetization and the short-range correlation functions in its vicinity using the exact solution of the model. In the critical regime above the triple point we observe a strong variation of all physical quantities on a low energy scale of order $1/\Delta$ induced by the transversal quantum fluctuations. We interpret this phenomenon starting from a strong-coupling perturbation theory about the highly degenerate ground state of the Ising chain at the triple point. From the perturbation theory we identify the relevant scaling of the magnetic field and of the temperature. Applying the scaling to the exact solutions we obtain explicit formulae for the magnetization and short-range correlation functions at low temperatures.Comment: 18 pages, 7 figures, v2: figures rearranged, v3: a typo correcte

Large distance asymptotic behavior of the emptiness formation probability of the XXZ spin-1/2 Heisenberg chain

Using its multiple integral representation, we compute the large distance asymptotic behavior of the emptiness formation probability of the XXZ spin-1/2 Heisenberg chain in the massless regime.Comment: LPENSL-TH-10, 8 page

Asymptotics of Toeplitz Determinants and the Emptiness Formation Probability for the XY Spin Chain

We study an asymptotic behavior of a special correlator known as the Emptiness Formation Probability (EFP) for the one-dimensional anisotropic XY spin-1/2 chain in a transverse magnetic field. This correlator is essentially the probability of formation of a ferromagnetic string of length $n$ in the antiferromagnetic ground state of the chain and plays an important role in the theory of integrable models. For the XY Spin Chain, the correlator can be expressed as the determinant of a Toeplitz matrix and its asymptotical behaviors for $n \to \infty$ throughout the phase diagram are obtained using known theorems and conjectures on Toeplitz determinants. We find that the decay is exponential everywhere in the phase diagram of the XY model except on the critical lines, i.e. where the spectrum is gapless. In these cases, a power-law prefactor with a universal exponent arises in addition to an exponential or Gaussian decay. The latter Gaussian behavior holds on the critical line corresponding to the isotropic XY model, while at the critical value of the magnetic field the EFP decays exponentially. At small anisotropy one has a crossover from the Gaussian to the exponential behavior. We study this crossover using the bosonization approach.Comment: 40 pages, 9 figures, 1 table. The poor quality of some figures is due to arxiv space limitations. If You would like to see the pdf with good quality figures, please contact Fabio Franchini at "[email protected]

Bethe ansatz for the three-layer Zamolodchikov model

This paper is a continuation of our previous work (solv-int/9903001). We obtain two more functional relations for the eigenvalues of the transfer matrices for the $sl(3)$ chiral Potts model at $q^2=-1$. This model, up to a modification of boundary conditions, is equivalent to the three-layer three-dimensional Zamolodchikov model. From these relations we derive the Bethe ansatz equations.Comment: 22 pages, LaTeX, 5 figure

Quantum Spin Chains and Riemann Zeta Function with Odd Arguments

Riemann zeta function is an important object of number theory. It was also used for description of disordered systems in statistical mechanics. We show that Riemann zeta function is also useful for the description of integrable model. We study XXX Heisenberg spin 1/2 anti-ferromagnet. We evaluate a probability of formation of a ferromagnetic string in the anti-ferromagnetic ground state in thermodynamics limit. We prove that for short strings the probability can be expressed in terms of Riemann zeta function with odd arguments.Comment: LaTeX, 7 page

String correlation functions of the spin-1/2 Heisenberg XXZ chain

We calculate certain string correlation functions, originally introduced as order parameters in integer spin chains, for the spin-1/2 XXZ Heisenberg chain at zero temperature and in the thermodynamic limit. For small distances, we obtain exact results from Bethe Ansatz and exact diagonalization, whereas in the large-distance limit, field-theoretical arguments yield an asymptotic algebraic decay. We also make contact with two-point spin-correlation functions in the asymptotic limit.Comment: 23 pages, 4 figures. An incomplete discussion on the limit to the spin-spin correlation function is corrected on page 1