70 research outputs found
Properties of the String Operator in the Eight-Vertex Model
The construction of creation operators of exact strings in eigenvectors of
the eight vertex model at elliptic roots of unity of the crossing parameter
which allow the generation of the complete set of degenerate eigenstates is
based on the conjecture that the 'naive' string operator vanishes. In this note
we present a proof of this conjecture. Furthermore we show that for chains of
odd length the string operator is either proportional to the symmetry operator
or vanishes depending on the precise form of the crossing parameter.Comment: 18 pages, typographic errors correcte
New Developments in the Eight Vertex Model
We demonstrate that the Q matrix introduced in Baxter's 1972 solution of the
eight vertex model has some eigenvectors which are not eigenvectors of the spin
reflection operator and conjecture a new functional equation for Q(v) which
both contains the Bethe equation that gives the eigenvalues of the transfer
matrix and computes the degeneracies of these eigenvalues.Comment: 12 pages. Final version which will be published in J. Stat. Phy
Dynamic correlations of antiferromagnetic spin-1/2 XXZ chains at arbitrary temperature from complete diagonalization
All eigenstates and eigenvalues are determined for the spin- 1/2 chain
for rings with up to N=16 spins, for anisotropies
, and 1. The dynamic spin pair correlations , the dynamic structure factors
, and the intermediate structure factors are
calculated for arbitrary temperature T. It is found, that for all T,
is mainly concentrated on the region , where is the upper boundary of the
two-spinon continuum, although excited states corresponding to a much broader
frequency spectrum contribute. This is also true for the Haldane-Shastry model
and the frustrated Heisenberg model. The intermediate structure factors
for show exponential decay for high T and large
q. Within the accessible time range, the time-dependent spin correlation
functions do not display the long-time signatures of spin diffusion.Comment: 30 pages, REVTEX, 21 figures, to appear in Physical Review
A new Q-matrix in the Eight-Vertex Model
We construct a -matrix for the eight-vertex model at roots of unity for
crossing parameter with odd , a case for which the existing
constructions do not work. The new -matrix \Q depends as usual on the
spectral parameter and also on a free parameter . For \Q has the
standard properties. For , however, it does not commute with the
operator and not with itself for different values of the spectral
parameter. We show that the six-vertex limit of \Q(v,t=iK'/2) exists.Comment: 10 pages section on quasiperiodicity added, typo corrected, published
versio
New Q matrices and their functional equations for the eight vertex model at elliptic roots of unity
The Q matrix invented by Baxter in 1972 to solve the eight vertex model at
roots of unity exists for all values of N, the number of sites in the chain,
but only for a subset of roots of unity. We show in this paper that a new Q
matrix, which has recently been introduced and is non zero only for N even,
exists for all roots of unity. In addition we consider the relations between
all of the known Q matrices of the eight vertex model and conjecture functional
equations for them.Comment: 20 pages, 2 Postscript figure
An elliptic current operator for the 8 vertex model
We compute the operator which creates the missing degenerate states in the
algebraic Bethe ansatz of the 8 vertex model at roots of unity and relate it to
the concept of an elliptic current operator. We find that in sharp contrast
with the corresponding formalism in the six-vertex model at roots of unity the
current operator is not nilpotent with the consequence that in the construction
of degenerate eigenstates of the transfer matrix an arbitrary number of exact
strings can be added to the set of regular Bethe roots. Thus the original set
of free parameters {s,t} of an eigenvector of T is enlarged to become
{s,t,\lambda_{c,1}, ..., \lambda_{c,n}\} with arbitrary string centers
\lambda_{c,j} and arbitrary n.Comment: 16 pages, Latex typographic errors corrected, text added, reference
added, accepted by Journal of Physics A,Mathematical and Genera
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