258 research outputs found
Higher particle form factors of branch point twist fields in integrable quantum field theories
In this paper we compute higher particle form factors of branch point twist
fields. These fields were first described in the context of massive
1+1-dimensional integrable quantum field theories and their correlation
functions are related to the bi-partite entanglement entropy. We find analytic
expressions for some form factors and check those expressions for consistency,
mainly by evaluating the conformal dimension of the corresponding twist field
in the underlying conformal field theory. We find that solutions to the form
factor equations are not unique so that various techniques need to be used to
identify those corresponding to the branch point twist field we are interested
in. The models for which we carry out our study are characterized by staircase
patterns of various physical quantities as functions of the energy scale. As
the latter is varied, the beta-function associated to these theories comes
close to vanishing at several points between the deep infrared and deep
ultraviolet regimes. In other words, renormalisation group flows approach the
vicinity of various critical points before ultimately reaching the ultraviolet
fixed point. This feature provides an optimal way of checking the consistency
of higher particle form factor solutions, as the changes on the conformal
dimension of the twist field at various energy scales can only be accounted for
by considering higher particle form factor contributions to the expansion of
certain correlation functions.Comment: 25 pages, 4 figures; v2 contains small correction
Boundary Quantum Field Theories with Infinite Resonance States
We extend a recent work by Mussardo and Penati on integrable quantum field
theories with a single stable particle and an infinite number of unstable
resonance states, including the presence of a boundary. The corresponding
scattering and reflection amplitudes are expressed in terms of Jacobian
elliptic functions, and generalize the ones of the massive thermal Ising model
and of the Sinh-Gordon model. In the case of the generalized Ising model we
explicitly study the ground state energy and the one-point function of the
thermal operator in the short-distance limit, finding an oscillating behaviour
related to the fact that the infinite series of boundary resonances does not
decouple from the theory even at very short-distance scales. The analysis of
the generalized Sinh-Gordon model with boundary reveals an interesting
constraint on the analytic structure of the reflection amplitude. The roaming
limit procedure which leads to the Ising model, in fact, can be consistently
performed only if we admit that the nature of the bulk spectrum uniquely fixes
the one of resonance states on the boundary.Comment: 18 pages, 11 figures, LATEX fil
Applications of quantum integrable systems
We present two applications of quantum integrable systems. First, we predict
that it is possible to generate high harmonics from solid state devices by
demostrating that the emission spectrum for a minimally coupled laser field of
frequency to an impurity system of a quantum wire, contains multiples
of the incoming frequency. Second, evaluating expressions for the conductance
in the high temperature regime we show that the caracteristic filling fractions
of the Jain sequence, which occur in the fractional quantum Hall effect, can be
obtained from quantum wires which are described by minimal affine Toda field
theories.Comment: 25 pages of LaTex, 4 figures, based on talk at the 6-th international
workshop on conformal field theories and integrable models, (Chernogolovka,
September 2002
Constructing Infinite Particle Spectra
We propose a general construction principle which allows to include an
infinite number of resonance states into a scattering matrix of hyperbolic
type. As a concrete realization of this mechanism we provide new S-matrices
generalizing a class of hyperbolic ones, which are related to a pair of simple
Lie algebras, to the elliptic case. For specific choices of the algebras we
propose elliptic generalizations of affine Toda field theories and the
homogeneous sine-Gordon models. For the generalization of the sinh-Gordon model
we compute explicitly renormalization group scaling functions by means of the
c-theorem and the thermodynamic Bethe ansatz. In particular we identify the
Virasoro central charges of the corresponding ultraviolet conformal field
theories.Comment: 7 pages Latex, 7 figures (typo in figure 3 corrected
Entropy inequalities from reflection positivity
We investigate the question of whether the entropy and the Renyi entropies of
the vacuum state reduced to a region of the space can be represented in terms
of correlators in quantum field theory. In this case, the positivity relations
for the correlators are mapped into inequalities for the entropies. We write
them using a real time version of reflection positivity, which can be
generalized to general quantum systems. Using this generalization we can prove
an infinite sequence of inequalities which are obeyed by the Renyi entropies of
integer index. There is one independent inequality involving any number of
different subsystems. In quantum field theory the inequalities acquire a simple
geometrical form and are consistent with the integer index Renyi entropies
being given by vacuum expectation values of twisting operators in the Euclidean
formulation. Several possible generalizations and specific examples are
analyzed.Comment: Significantly enlarged and corrected version. Counterexamples found
for the most general form of the inequalities. V3: minor change
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 RĂ©nyi entropies at large times mt â« 1 emerges from a perturbative calculation at second order. We also show that the RĂ©nyi and von Neumann entropies, in infinite volume, contain subleading oscillatory contributions of frequency 2m and amplitude proportional to (mt)â3/2. 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
Arguments towards a c-theorem from branch-point twist fields
A fundamental quantity in 1+1 dimensional quantum field theories is
Zamolodchikov's c-function. A function of a renormalization group distance
parameter r that interpolates between UV and IR fixed points, its value is
usually interpreted as a measure of the number of degrees of freedom of a model
at a particular energy scale. The c-theorem establishes that c(r) is a
monotonically decreasing function of r and that its derivative may only vanish
at quantum critical points. At those points c(r) becomes the central charge of
the conformal field theory which describes the critical point. In this letter
we argue that a different function proposed by Calabrese and Cardy, defined in
terms of the two-point function of a branch point twist field and the trace of
the stress-energy tensor, has exactly the same qualitative features as c(r).Comment: 10 page
Bi-partite entanglement entropy in integrable models with backscattering
In this paper we generalise the main result of a recent work by J. L. Cardy
and the present authors concerning the bi-partite entanglement entropy between
a connected region and its complement. There the expression of the leading
order correction to saturation in the large distance regime was obtained for
integrable quantum field theories possessing diagonal scattering matrices. It
was observed to depend only on the mass spectrum of the model and not on the
specific structure of the diagonal scattering matrix. Here we extend that
result to integrable models with backscattering (i.e. with non-diagonal
scattering matrices). We use again the replica method, which connects the
entanglement entropy to partition functions on Riemann surfaces with two branch
points. Our main conclusion is that the mentioned infrared correction takes
exactly the same form for theories with and without backscattering. In order to
give further support to this result, we provide a detailed analysis in the
sine-Gordon model in the coupling regime in which no bound states (breathers)
occur. As a consequence, we obtain the leading correction to the sine-Gordon
partition function on a Riemann surface in the large distance regime.
Observations are made concerning the limit of large number of sheets.Comment: 22 pages, 2 figure
Supersymmetric integrable scattering theories with unstable particles
We propose scattering matrices for N=1 supersymmetric integrable quantum
field theories in 1+1 dimensions which involve unstable particles in their
spectra. By means of the thermodynamic Bethe ansatz we analyze the ultraviolet
behaviour of some of these theories and identify the effective Virasoro central
charge of the underlying conformal field theories.Comment: 15 pages Late
Bi-partite entanglement entropy in massive (1+1)-dimensional quantum field theories
This paper is a review of the main results obtained in a series of papers involving the present authors and their collaborator J L Cardy over the last 2 years. In our work, we have developed and applied a new approach for the computation of the bi-partite entanglement entropy in massive (1+1)-dimensional quantum field theories. In most of our work we have also considered these theories to be integrable. Our approach combines two main ingredients: the 'replica trick' and form factors for integrable models and more generally for massive quantum field theory. Our basic idea for combining fruitfully these two ingredients is that of the branch-point twist field. By the replica trick, we obtained an alternative way of expressing the entanglement entropy as a function of the correlation functions of branch-point twist fields. On the other hand, a generalization of the form factor program has allowed us to study, and in integrable cases to obtain exact expressions for, form factors of such twist fields. By the usual decomposition of correlation functions in an infinite series involving form factors, we obtained exact results for the infrared behaviours of the bi-partite entanglement entropy, and studied both its infrared and ultraviolet behaviours for different kinds of models: with and without boundaries and backscattering, at and out of integrability
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