8 research outputs found
Critical interfaces of the Ashkin-Teller model at the parafermionic point
We present an extensive study of interfaces defined in the Z_4 spin lattice
representation of the Ashkin-Teller (AT) model. In particular, we numerically
compute the fractal dimensions of boundary and bulk interfaces at the
Fateev-Zamolodchikov point. This point is a special point on the self-dual
critical line of the AT model and it is described in the continuum limit by the
Z_4 parafermionic theory. Extending on previous analytical and numerical
studies [10,12], we point out the existence of three different values of
fractal dimensions which characterize different kind of interfaces. We argue
that this result may be related to the classification of primary operators of
the parafermionic algebra. The scenario emerging from the studies presented
here is expected to unveil general aspects of geometrical objects of critical
AT model, and thus of c=1 critical theories in general.Comment: 15 pages, 3 figure
Conformal Curves in Potts Model: Numerical Calculation
We calculated numerically the fractal dimension of the boundaries of the
Fortuin-Kasteleyn clusters of the -state Potts model for integer and
non-integer values of on the square lattice.
In addition we calculated with high accuracy the fractal dimension of the
boundary points of the same clusters on the square domain. Our calculation
confirms that this curves can be described by SLE.Comment: 11 Pages, 4 figure
Three Dimensional Ising Model, Percolation Theory and Conformal Invariance
The fractal structure and scaling properties of a 2d slice of the 3d Ising
model is studied using Monte Carlo techniques. The percolation transition of
geometric spin (GS) clusters is found to occur at the Curie point, reflecting
the critical behavior of the 3d model. The fractal dimension and the winding
angle statistics of the perimeter and external perimeter of the geometric spin
clusters at the critical point suggest that, if conformally invariant in the
scaling limit, they can be described by the theory of Schramm-Loewner evolution
(SLE_\kappa) with diffusivity of \kappa=5 and 16/5, respectively, putting them
in the same universality class as the interfaces in 2d tricritical Ising model.
It is also found that the Fortuin-Kasteleyn (FK) clusters associated with the
cross sections undergo a nontrivial percolation transition, in the same
universality class as the ordinary 2d critical percolation.Comment: 5 pages, 5 figures, accepted for publication in EuroPhysics Letters
(EPL
On R\ue9nyi entropies of disjoint intervals in conformal field theory
We study the R\ue9nyi entropies of N disjoint intervals in the conformal field theories describing the free compactified boson and the Ising model. They are computed as the 2N-point function of twist fields, by employing the partition function of the model on a particular class of Riemann surfaces. The results are written in terms of Riemann theta functions. The prediction for the free boson in the decompactification regime is checked against exact results for the harmonic chain. For the Ising model, matrix product state computations agree with the conformal field theory result once the finite size corrections have been taken into account. \ua9 2014 IOP Publishing Ltd and SISSA Medialab srl
Entanglement negativity in the critical Ising chain
We study the scaling of the traces of the integer powers of the partially transposed reduced density matrix Tr(rho(T2)(A))Th and of the entanglement negativity for two spin blocks as a function of their length and separation in the critical Ising chain. For two adjacent blocks, we show that tensor network calculations agree with universal conformal field theory (CFT) predictions. In the case of two disjoint blocks the CFT predictions are recovered only after taking into account the finite size corrections induced by the finite length of the blocks
Entanglement negativity in extended systems: a field theoretical approach
We report on a systematic approach for the calculation of the negativity in the ground state of a one-dimensional quantum field theory. The partial transpose rho(T2)(A) of the reduced density matrix of a subsystem A = A(1) boolean OR A(2) is explicitly constructed as an imaginary-time path integral and from this the replicated traces Tr(rho(T2)(A))(n) are obtained. The logarithmic negativity epsilon = log parallel to rho(T2)(A)parallel to is then the continuation to n --> 1 of the traces of the even powers. For pure states, this procedure reproduces the known results. We then apply this method to conformally invariant field theories (CFTs) in several different physical situations for infinite and finite systems and without or with boundaries. In particular, in the case of two adjacent intervals of lengths l(1), l(2) in an infinite system, we derive the result epsilon similar to (c/4) ln(l(1)l(2)/(l(1) + l(2))), where c is the central charge. For the more complicated case of two disjoint intervals, we show that the negativity depends only on the harmonic ratio of the four end points and so is manifestly scale invariant. We explicitly calculate the scale invariant functions for the replicated traces in the case of the CFT for the free compactified boson, but we have not so far been able to obtain the n --> 1 continuation for the negativity even in the limit of large compactification radius. We have checked all our findings against exact numerical results for the harmonic chain which is described by a non-compactified free boson
Entanglement Entropy from a Holographic Viewpoint
The entanglement entropy has been historically studied by many authors in
order to obtain quantum mechanical interpretations of the gravitational
entropy. The discovery of AdS/CFT correspondence leads to the idea of
holographic entanglement entropy, which is a clear solution to this important
problem in gravity. In this article, we would like to give a quick survey of
recent progresses on the holographic entanglement entropy. We focus on its
gravitational aspects, so that it is comprehensible to those who are familiar
with general relativity and basics of quantum field theory.Comment: Latex, 30 pages, invited review for Classical and Quantum Gravity,
minor correction