567 research outputs found
Fusion of \ade Lattice Models
Fusion hierarchies of \ade face models are constructed. The fused critical
, and elliptic models yield new solutions of the Yang-Baxter
equations with bond variables on the edges of faces in addition to the spin
variables on the corners. It is shown directly that the row transfer matrices
of the fused models satisfy special functional equations. Intertwiners between
the fused \ade models are constructed by fusing the cells that intertwine the
elementary face weights. As an example, we calculate explicitly the fused
face weights of the 3-state Potts model associated with the
diagram as well as the fused intertwiner cells for the --
intertwiner. Remarkably, this fusion yields the face weights of
both the Ising model and 3-state CSOS models.Comment: 41 page
Intertwiners and \ade Lattice Models
Intertwiners between \ade lattice models are presented and the general theory
developed. The intertwiners are discussed at three levels: at the level of the
adjacency matrices, at the level of the cell calculus intertwining the face
algebras and at the level of the row transfer matrices. A convenient graphical
representation of the intertwining cells is introduced. The utility of the
intertwining relations in studying the spectra of the \ade models is
emphasized. In particular, it is shown that the existence of an intertwiner
implies that many eigenvalues of the \ade row transfer matrices are exactly in
common for a finite system and, consequently, that the corresponding central
charges and scaling dimensions can be identified.Comment: 48 pages, Two postscript files included
An Ising model in a magnetic field with a boundary
We obtain the diagonal reflection matrices for a recently introduced family
of dilute lattice models in which the model can be
viewed as an Ising model in a magnetic field. We calculate the surface free
energy from the crossing-unitarity relation and thus directly obtain the
critical magnetic surface exponent for odd and surface specific
heat exponent for even in each of the various regimes. For in the
appropriate regime we obtain the Ising exponent ,
which is the first determination of this exponent without the use of scaling
relations.Comment: 7 pages, LaTe
Multipartite entanglement purification with quantum nondemolition detectors
We present a scheme for multipartite entanglement purification of quantum
systems in a Greenberger-Horne-Zeilinger state with quantum nondemolition
detectors (QNDs). This scheme does not require the controlled-not gates which
cannot be implemented perfectly with linear optical elements at present, but
QNDs based on cross-Kerr nonlinearities. It works with two steps, i.e., the
bit-flipping error correction and the phase-flipping error correction. These
two steps can be iterated perfectly with parity checks and simple single-photon
measurements. This scheme does not require the parties to possess sophisticated
single photon detectors. These features maybe make this scheme more efficient
and feasible than others in practical applications.Comment: 8 pages, 5 figure
Surface Critical Phenomena in Interaction-Round-a-Face Models
A general scheme has been proposed to study the critical behaviour of
integrable interaction-round-a-face models with fixed boundary conditions. It
has been shown that the boundary crossing symmetry plays an important role in
determining the surface free energy. The surface specific heat exponent can
thus be obtained without explicitly solving the reflection equations for the
boundary face weights. For the restricted SOS -state models of Andrews,
Baxter and Forrester the surface specific heat exponent is found to be
.Comment: 11 pages; Latex fil
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