94 research outputs found
Finite Volume Spectrum of Sine-Gordon Model and its Restrictions
In this thesis, we review recent progresses on Nonlinear Integral Equation
approach to finite size effects in two dimensional integrable quantum field
theories, with emphasis to Sine-Gordon/Massive Thirring model and restrictions
to minimal models perturbed by . Exact calculations of the
dependence of energy levels on the size are presented for vacuum and many
excited states.Comment: PhD thesis, 96 pages, 28 figure
Scaling Functions in the Odd Charge Sector of Sine-Gordon/Massive Thirring Theory
A non-linear integral equation (NLIE) governing the finite size effects of
excited states of even topological charge in the sine-Gordon (sG) / massive
Thirring (mTh) field theory, deducible from a light-cone lattice formulation of
the model, has been known for some time. In this letter we conjecture an
extension of this NLIE to states with odd topological charge, thus completing
the spectrum of the theory. The scaling functions obtained as solutions to our
conjectured NLIE are compared successfully with Truncated Conformal Space data
and the construction is shown to be compatible with all other facts known about
the local Hilbert spaces of sG and mTh models. With the present results we have
achieved a full control over the finite size behaviour of energy levels of
sG/mTh theory.Comment: LaTeX2e, 12 pp., 3 eps figs. Remarks on locality adde
Nonperturbative study of the two-frequency sine-Gordon model
The two-frequency sine-Gordon model is examined. The focus is mainly on the
case when the ratio of the frequencies is 1/2, given the recent interest in the
literature. We discuss the model both in a perturbative (form factor
perturbation theory) and a nonperturbative (truncated conformal space approach)
framework, and give particular attention to a phase transition conjectured
earlier by Delfino and Mussardo. We give substantial evidence that the
transition is of second order and that it is in the Ising universality class.
Furthermore, we check the UV-IR operator correspondence and conjecture the
phase diagram of the theory.Comment: Minor corrections, LaTeX2e, 39 pages, 26 figures (4 pslatex, 1
postscript and 21 eps
Excited Boundary TBA in the Tricritical Ising Model
By considering the continuum scaling limit of the RSOS lattice model
of Andrews-Baxter-Forrester with integrable boundaries, we derive excited state
TBA equations describing the boundary flows of the tricritical Ising model.
Fixing the bulk weights to their critical values, the integrable boundary
weights admit a parameter which plays the role of the perturbing
boundary field and induces the renormalization group flow between
boundary fixed points. The boundary TBA equations determining the RG flows are
derived in the example. The
induced map between distinct Virasoro characters of the theory are specified in
terms of distribution of zeros of the double row transfer matrix.Comment: Latex, 14 pages - Talk given at the Landau meeting "CFT and
Integrable Models", Sept. 2002 - v2: some statements about
perturbations correcte
On the commuting charges for the highest dimension SU(2) operators in planar SYM
We consider the highest anomalous dimension operator in the SU(2) sector of
planar SYM at all-loop, though neglecting wrapping contributions.
In any case, the latter enter the loop expansion only after a precise
length-depending order. In the thermodynamic limit we write both a linear
integral equation for the Bethe root density and a linear system obeyed by the
commuting charges. Consequently, we determine the leading strong coupling
contribution to the density and from this an approximation to the leading and
sub-leading terms of any charge : it scales as , which
generalises the Gubser-Klebanov-Polyakov energy law. In the end, we briefly
extend these considerations to finite lengths and 'excited' operators by using
the idea of a non-linear integral equation.Comment: Latex file, 20 pages, some typos corrected, some technical details
expanded and explaine
Nonlinear Integral Equation and Finite Volume Spectrum of Minimal Models Perturbed by
We describe an extension of the nonlinear integral equation (NLIE) method to
Virasoro minimal models perturbed by the relevant operator \Phi_{(1,3). Along
the way, we also complete our previous studies of the finite volume spectrum of
sine-Gordon theory by considering the attractive regime and more specifically,
breather states. For the minimal models, we examine the states with zero
topological charge in detail, and give numerical comparison to TBA and TCS
results. We think that the evidence presented strongly supports the validity of
the NLIE description of perturbed minimal models.Comment: 31 pages, latex (LyX generated). One reference and few comments adde
Stable particles in anisotropic spin-1 chains
Motivated by field-theoretic predictions we investigate the stable
excitations that exist in two characteristic gapped phases of a spin-1 model
with Ising-like and single-ion anisotropies. The sine-Gordon theory indicates a
region close to the phase boundary where a stable breather exists besides the
stable particles, that form the Haldane triplet at the Heisenberg isotropic
point. The numerical data, obtained by means of the Density Matrix
Renormalization Group, confirm this picture in the so-called large-D phase for
which we give also a quantitative analysis of the bound states using standard
perturbation theory. However, the situation turns out to be considerably more
intricate in the Haldane phase where, to the best of our data, we do not
observe stable breathers contrarily to what could be expected from the
sine-Gordon model, but rather only the three modes predicted by a novel
anisotropic extension of the Non-Linear Sigma Model studied here by means of a
saddle-point approximation.Comment: 8 pages, 7 eps figures, svjour clas
Form factor perturbation theory from finite volume
Using a regularization by putting the system in finite volume, we develop a
novel approach to form factor perturbation theory for nonintegrable models
described as perturbations of integrable ones. This permits to go beyond first
order in form factor perturbation theory and in principle works to any order.
The procedure is carried out in detail for double sine-Gordon theory, where the
vacuum energy density and breather mass correction is evaluated at second
order. The results agree with those obtained from the truncated conformal space
approach. The regularization procedure can also be used to compute other
spectral sums involving disconnected pieces of form factors such as those that
occur e.g. in finite temperature correlators.Comment: 14 pages, no figures, LaTeX2e file, v2: typos corrected, references
and discussion of further details adde
Super-Hubbard models and applications
We construct XX- and Hubbard- like models based on unitary superalgebras
gl(N|M) generalising Shastry's and Maassarani's approach of the algebraic case.
We introduce the R-matrix of the gl(N|M) XX model and that of the Hubbard model
defined by coupling two independent XX models. In both cases, we show that the
R-matrices satisfy the Yang--Baxter equation, we derive the corresponding local
Hamiltonian in the transfer matrix formalism and we determine the symmetry of
the Hamiltonian. Explicit examples are worked out. In the cases of the gl(1|2)
and gl(2|2) Hubbard models, a perturbative calculation at two loops a la Klein
and Seitz is performed.Comment: 26 page
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