263 research outputs found
LeClair-Mussardo series for two-point functions in Integrable QFT
We develop a well-defined spectral representation for two-point functions in
relativistic Integrable QFT in finite density situations, valid for space-like
separations. The resulting integral series is based on the infinite volume,
zero density form factors of the theory, and certain statistical functions
related to the distribution of Bethe roots in the finite density background.
Our final formulas are checked by comparing them to previous partial results
obtained in a low-temperature expansion. It is also show that in the limit of
large separations the new integral series factorizes into the product of two
LeClair-Mussardo series for one-point functions, thereby satisfying the
clustering requirement for the two-point function.Comment: 27 pages, v2: minor modifications, a note and a reference adde
Bethe Ansatz Matrix Elements as Non-Relativistic Limits of Form Factors of Quantum Field Theory
We show that the matrix elements of integrable models computed by the
Algebraic Bethe Ansatz can be put in direct correspondence with the Form
Factors of integrable relativistic field theories. This happens when the
S-matrix of a Bethe Ansatz model can be regarded as a suitable non-relativistic
limit of the S-matrix of a field theory, and when there is a well-defined
mapping between the Hilbert spaces and operators of the two theories. This
correspondence provides an efficient method to compute matrix elements of Bethe
Ansatz integrable models, overpassing the technical difficulties of their
direct determination. We analyze this correspondence for the simplest example
in which it occurs, i.e. the Quantum Non-Linear Schrodinger and the Sinh-Gordon
models.Comment: 10 page
On Form Factors in nested Bethe Ansatz systems
We investigate form factors of local operators in the multi-component Quantum
Non-linear Schr\"odinger model, a prototype theory solvable by the so-called
nested Bethe Ansatz. We determine the analytic properties of the infinite
volume form factors using the coordinate Bethe Ansatz solution and we establish
a connection with the finite volume matrix elements. In the two-component
models we derive a set of recursion relations for the "magnonic form factors",
which are the matrix elements on the nested Bethe Ansatz states. In certain
simple cases (involving states with only one spin-impurity) we obtain explicit
solutions for the recursion relations.Comment: 34 pages, v2 (minor modifications
Tensor network decompositions for absolutely maximally entangled states
Absolutely maximally entangled (AME) states of qudits (also known as
perfect tensors) are quantum states that have maximal entanglement for all
possible bipartitions of the sites/parties. We consider the problem of whether
such states can be decomposed into a tensor network with a small number of
tensors, such that all physical and all auxiliary spaces have the same
dimension . We find that certain AME states with can be decomposed
into a network with only three 4-leg tensors; we provide concrete solutions for
local dimension and higher. Our result implies that certain AME states
with six parties can be created with only three two-site unitaries from a
product state of three Bell pairs, or equivalently, with six two-site unitaries
acting on a product state on six qudits. We also consider the problem for
, where we find similar tensor network decompositions with six 4-leg
tensors.Comment: 21 page
Determining matrix elements and resonance widths from finite volume: the dangerous mu-terms
The standard numerical approach to determining matrix elements of local
operators and width of resonances uses the finite volume dependence of energy
levels and matrix elements. Finite size corrections that decay exponentially in
the volume are usually neglected or taken into account using perturbation
expansion in effective field theory. Using two-dimensional sine-Gordon field
theory as "toy model" it is shown that some exponential finite size effects
could be much larger than previously thought, potentially spoiling the
determination of matrix elements in frameworks such as lattice QCD. The
particular class of finite size corrections considered here are mu-terms
arising from bound state poles in the scattering amplitudes. In sine-Gordon
model, these can be explicitly evaluated and shown to explain the observed
discrepancies to high precision. It is argued that the effects observed are not
special to the two-dimensional setting, but rather depend on general field
theoretic features that are common with models relevant for particle physics.
It is important to understand these finite size corrections as they present a
potentially dangerous source of systematic errors for the determination of
matrix elements and resonance widths.Comment: 26 pages, 13 eps figures, LaTeX2e fil
Form factor expansion for thermal correlators
We consider finite temperature correlation functions in massive integrable
Quantum Field Theory. Using a regularization by putting the system in finite
volume, we develop a novel approach (based on multi-dimensional residues) to
the form factor expansion for thermal correlators. The first few terms are
obtained explicitly in theories with diagonal scattering. We also discuss the
validity of the LeClair-Mussardo proposal.Comment: 41 pages; v2: minor corrections, v3: minor correction
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