285 research outputs found
Low-Temperature Expansions and Correlation Functions of the Z_3-Chiral Potts Model
Using perturbative methods we derive new results for the spectrum and
correlation functions of the general Z_3-chiral Potts quantum chain in the
massive low-temperature phase. Explicit calculations of the ground state energy
and the first excitations in the zero momentum sector give excellent
approximations and confirm the general statement that the spectrum in the
low-temperature phase of general Z_n-spin quantum chains is identical to one in
the high-temperature phase where the role of charge and boundary conditions are
interchanged. Using a perturbative expansion of the ground state for the Z_3
model we are able to gain some insight in correlation functions. We argue that
they might be oscillating and give estimates for the oscillation length as well
as the correlation length.Comment: 17 pages (Plain TeX), BONN-HE-93-1
Form-factors in the Baxter-Bazhanov-Stroganov model I: Norms and matrix elements
We continue our investigation of the Z_N-Baxter-Bazhanov-Stroganov model
using the method of separation of variables [nlin/0603028]. In this paper we
calculate the norms and matrix elements of a local Z_N-spin operator between
eigenvectors of the auxiliary problem. For the norm the multiple sums over the
intermediate states are performed explicitly. In the case N=2 we solve the
Baxter equation and obtain form-factors of the spin operator of the periodic
Ising model on a finite lattice.Comment: 24 page
Transfer matrix eigenvectors of the Baxter-Bazhanov-Stroganov -model for N=2
We find a representation of the row-to-row transfer matrix of the
Baxter-Bazhanov-Stroganov -model for N=2 in terms of an integral over
two commuting sets of grassmann variables. Using this representation, we
explicitly calculate transfer matrix eigenvectors and normalize them. It is
also shown how form factors of the model can be expressed in terms of
determinants and inverses of certain Toeplitz matrices.Comment: 23 page
Spin operator matrix elements in the quantum Ising chain: fermion approach
Using some modification of the standard fermion technique we derive
factorized formula for spin operator matrix elements (form-factors) between
general eigenstates of the Hamiltonian of quantum Ising chain in a transverse
field of finite length. The derivation is based on the approach recently used
to derive factorized formula for Z_N-spin operator matrix elements between
ground eigenstates of the Hamiltonian of the Z_N-symmetric superintegrable
chiral Potts quantum chain. The obtained factorized formulas for the matrix
elements of Ising chain coincide with the corresponding expressions obtained by
the Separation of Variables Method.Comment: 19 page
Multi-particle structure in the Z_n-chiral Potts models
We calculate the lowest translationally invariant levels of the Z_3- and
Z_4-symmetrical chiral Potts quantum chains, using numerical diagonalization of
the hamiltonian for N <= 12 and N <= 10 sites, respectively, and extrapolating
N to infinity. In the high-temperature massive phase we find that the pattern
of the low-lying zero momentum levels can be explained assuming the existence
of n-1 particles carrying Z_n-charges Q = 1, ... , n-1 (mass m_Q), and their
scattering states. In the superintegrable case the masses of the n-1 particles
become proportional to their respective charges: m_Q = Q m_1. Exponential
convergence in N is observed for the single particle gaps, while power
convergence is seen for the scattering levels. We also verify that
qualitatively the same pattern appears for the self-dual and integrable cases.
For general Z_n we show that the energy-momentum relations of the particles
show a parity non-conservation asymmetry which for very high temperatures is
exclusive due to the presence of a macroscopic momentum P_m=(1-2Q/n)/\phi,
where \phi is the chiral angle and Q is the Z_n-charge of the respective
particle.Comment: 22 pages (LaTeX) plus 5 figures (included as PostScript),
BONN-HE-92-3
Minimal Unitary Models and The Closed SU(2)-q Invariant Spin Chain
We consider the Hamiltonian of the closed invariant chain. We
project a particular class of statistical models belonging to the unitary
minimal series. A particular model corresponds to a particular value of the
coupling constant. The operator content is derived. This class of models has
charge-dependent boundary conditions. In simple cases (Ising, 3-state Potts)
corresponding Hamiltonians are constructed. These are non-local as the original
spin chain.Comment: 19 pages, latex, no figure
Spin operator matrix elements in the superintegrable chiral Potts quantum chain
We derive spin operator matrix elements between general eigenstates of the
superintegrable Z_N-symmetric chiral Potts quantum chain of finite length. Our
starting point is the extended Onsager algebra recently proposed by R.Baxter.
For each pair of spaces (Onsager sectors) of the irreducible representations of
the Onsager algebra, we calculate the spin matrix elements between the
eigenstates of the Hamiltonian of the quantum chain in factorized form, up to
an overall scalar factor. This factor is known for the ground state Onsager
sectors. For the matrix elements between the ground states of these sectors we
perform the thermodynamic limit and obtain the formula for the order
parameters. For the Ising quantum chain in a transverse field (N=2 case) the
factorized form for the matrix elements coincides with the corresponding
expressions obtained recently by the Separation of Variables Method.Comment: 24 pages, 1 figur
The modified tetrahedron equation and its solutions
A large class of 3-dimensional integrable lattice spin models is constructed.
The starting point is an invertible canonical mapping operator in the space of
a triple Weyl algebra. This operator is derived postulating a current branching
principle together with a Baxter Z-invariance. The tetrahedron equation for
this operator follows without further calculations. If the Weyl parameter is
taken to be a root of unity, the mapping operator decomposes into a matrix
conjugation and a C-number functional mapping. The operator of the matrix
conjugation satisfies a modified tetrahedron equation (MTE) in which the
"rapidities" are solutions of a classical integrable Hirota-type equation. The
matrix elements of this operator can be represented in terms of the
Bazhanov-Baxter Fermat curve cyclic functions, or alternatively in terms of
Gauss functions. The paper summarizes several recent publications on the
subject.Comment: 24 pages, 6 figures using epic/eepic package, Contribution to the
proceedings of the 6th International Conference on CFTs and Integrable
Models, Chernogolovka, Spetember 2002, reference adde
Form-factors in the Baxter-Bazhanov-Stroganov model II: Ising model on the finite lattice
We continue our investigation of the Baxter-Bazhanov-Stroganov or
\tau^{(2)}-model using the method of separation of variables
[nlin/0603028,arXiv:0708.4342]. In this paper we derive for the first time the
factorized formula for form-factors of the Ising model on a finite lattice
conjectured previously by A.Bugrij and O.Lisovyy in
[arXiv:0708.3625,arXiv:0708.3643]. We also find the matrix elements of the spin
operator for the finite quantum Ising chain in a transverse field.Comment: 25 pages; sections 8 and A.2 are extended, 2 related references are
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