29 research outputs found
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
- 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
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 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 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 chiral Potts model at . 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