37 research outputs found
Entanglement entropies of minimal models from null-vectors
We present a new method to compute R\'enyi entropies in one-dimensional
critical systems. The null-vector conditions on the twist fields in the cyclic
orbifold allow us to derive a differential equation for their correlation
functions. The latter are then determined by standard bootstrap techniques. We
apply this method to the calculation of various R\'enyi entropies in the
non-unitary Yang-Lee model.Comment: 43 pages, 7 figure
Three-point functions in c <= 1 Liouville theory and conformal loop ensembles
The possibility of extending the Liouville Conformal Field Theory from values
of the central charge to has been debated for many years
in condensed matter physics as well as in string theory. It was only recently
proven that such an extension -- involving a real spectrum of critical
exponents as well as an analytic continuation of the DOZZ formula for
three-point couplings -- does give rise to a consistent theory. We show in this
Letter that this theory can be interpreted in terms of microscopic loop models.
We introduce in particular a family of geometrical operators, and, using an
efficient algorithm to compute three-point functions from the lattice, we show
that their operator algebra corresponds exactly to that of vertex operators
in Liouville. We interpret geometrically the
limit of and explain why it is not the
identity operator (despite having conformal weight ).Comment: 11 pages, 6 figures. Version 2: minor improvement
Finite-Size Left-Passage Probability in Percolation
We obtain an exact finite-size expression for the probability that a percolation hull will touch the boundary, on a strip of finite width. In terms of clusters, this corresponds to the one-arm probability. Our calculation is based on the q-deformed Knizhnik-Zamolodchikov approach, and the results are expressed in terms of symplectic characters. In the large size limit, we recover the scaling behaviour predicted by Schramm's left-passage formula. We also derive a general relation between the left-passage probability in the Fortuin-Kasteleyn cluster model and the magnetisation profile in the open XXZ chain with diagonal, complex boundary term
A staggered six-vertex model with non-compact continuum limit
The antiferromagnetic critical point of the Potts model on the square lattice
was identified by Baxter as a staggered integrable six-vertex model. In this
work, we investigate the integrable structure of this model. It enables us to
derive some new properties, such as the Hamiltonian limit of the model, an
equivalent vertex model, and the structure resulting from the Z_2 symmetry.
Using this material, we discuss the low-energy spectrum, and relate it to
geometrical excitations. We also compute the critical exponents by solving the
Bethe equations for a large lattice width N. The results confirm that the
low-energy spectrum is a collection of continua with typical exponent gaps of
order 1/(log N)^2.Comment: 46 pages, 31 figure
Finite-size corrections in critical symmetry-resolved entanglement
In the presence of a conserved quantity, symmetry-resolved entanglement
entropies are a refinement of the usual notion of entanglement entropy of a
subsystem. For critical 1d quantum systems, it was recently shown in various
contexts that these quantities generally obey entropy equipartition in the
scaling limit, i.e. they become independent of the symmetry sector.
In this paper, we examine the finite-size corrections to the entropy
equipartition phenomenon, and show that the nature of the symmetry group plays
a crucial role. In the case of a discrete symmetry group, the corrections decay
algebraically with system size, with exponents related to the operators'
scaling dimensions. In contrast, in the case of a U(1) symmetry group, the
corrections only decay logarithmically with system size, with model-dependent
prefactors. We show that the determination of these prefactors boils down to
the computation of twisted overlaps.Comment: 19 pages + Appendix, 5 figure