43,390 research outputs found
On dilatation operator for a renormalizable theory
Given a renormalizable theory we construct the dilatation operator, in the
sense of generator of RG flow of composite operators. The generator is found as
a differential operator acting on the space of normal symbols of composite
operators in the theory. In the spirit of AdS/CFT correspondence, this operator
is interpreted as the Hamiltonian of the dual theory. In the case of a field
theory with non-abelian gauge symmetry the resulting system is a matrix model.
The one-loop case is analyzed in details and it is shown that we reproduce
known results from N=4 supersymmetric Yang-Mills theory.Comment: 26 pages, no figure
Entanglement Dynamics after a Quench in Ising Field Theory: A Branch Point Twist Field Approach
We extend the branch point twist field approach for the calculation of entanglement entropies to time-dependent problems in 1+1-dimensional massive quantum field theories. We focus on the simplest example: a mass quench in the Ising field theory from initial mass m0 to final mass m. The main analytical results are obtained from a perturbative expansion of the twist field one-point function in the post-quench quasi-particle basis. The expected linear growth of the Rényi entropies at large times mt ≫ 1 emerges from a perturbative calculation at second order. We also show that the Rényi and von Neumann entropies, in infinite volume, contain subleading oscillatory contributions of frequency 2m and amplitude proportional to (mt)−3/2. The oscillatory terms are correctly predicted by an alternative perturbation series, in the pre-quench quasi-particle basis, which we also discuss. A comparison to lattice numerical calculations carried out on an Ising chain in the scaling limit shows very good agreement with the quantum field theory predictions. We also find evidence of clustering of twist field correlators which implies that the entanglement entropies are proportional to the number of subsystem boundary points
Aperiodic Ising Quantum Chains
Some years ago, Luck proposed a relevance criterion for the effect of
aperiodic disorder on the critical behaviour of ferromagnetic Ising systems. In
this article, we show how Luck's criterion can be derived within an exact
renormalisation scheme for Ising quantum chains with coupling constants
modulated according to substitution rules. Luck's conjectures for this case are
confirmed and refined. Among other outcomes, we give an exact formula for the
correlation length critical exponent for arbitrary two-letter substitution
sequences with marginal fluctuations of the coupling constants.Comment: 27 pages, LaTeX, 1 Postscript figure included, using epsf.sty and
amssymb.sty (one error corrected, some minor changes
Integrability and conformal data of the dimer model
The central charge of the dimer model on the square lattice is still being
debated in the literature. In this paper, we provide evidence supporting the
consistency of a description. Using Lieb's transfer matrix and its
description in terms of the Temperley-Lieb algebra at , we
provide a new solution of the dimer model in terms of the model of critical
dense polymers on a tilted lattice and offer an understanding of the lattice
integrability of the dimer model. The dimer transfer matrix is analysed in the
scaling limit and the result for is expressed in terms of
fermions. Higher Virasoro modes are likewise constructed as limits of elements
of and are found to yield a realisation of the Virasoro algebra,
familiar from fermionic ghost systems. In this realisation, the dimer Fock
spaces are shown to decompose, as Virasoro modules, into direct sums of
Feigin-Fuchs modules, themselves exhibiting reducible yet indecomposable
structures. In the scaling limit, the eigenvalues of the lattice integrals of
motion are found to agree exactly with those of the conformal integrals
of motion. Consistent with the expression for obtained from
the transfer matrix, we also construct higher Virasoro modes with and
find that the dimer Fock space is completely reducible under their action.
However, the transfer matrix is found not to be a generating function for the
integrals of motion. Although this indicates that Lieb's transfer matrix
description is incompatible with the interpretation, it does not rule out
the existence of an alternative, compatible, transfer matrix description
of the dimer model.Comment: 54 pages. v2: minor correction
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