Plenary talks
Ahn Changrim
3-point functions of finite-size (dyonic) Giant magnons
We present holographic three-point correlation functions or structure
constants of a zero-momentum dilaton operator and two (dyonic) giant
magnon string states with a finite-size length in the semiclassical
approximation. We show that the semiclassical structure constants match
exactly with the three-point functions between two su(2) magnon single
trace operators with finite size and the Lagrangian in the large ’t
Hooft coupling constant limit. A special limit J>>√λ of our result
is compared with the relevant result based on the Lüscher corrections.
Bazhanov Vladimir
Generalized Mathieu Equation: An unpublished work by Alexei Zamolodchikov.
I will present an unpublished paper by Alyosha Zamolodchikov on
connection of the Sinh-Gordon model with the spectral theory of
differential equations.
Belavin Alexander
Instantons and 2d SUSY Conformal field theory
The correspondence between 4-dimensional $N=2$ SUSY $SU(k)$ gauge
theories on $R4/Z_m$ and $SU(k)$ Toda-like theories with $Z_m$
parafermionic symmetry is used to construct four-point $N=1$ super
Liouville conformal block, which corresponds to the particular case
$k=m=2$. The construction is based on the conjectural relation between
moduli spaces of $SU(2)$ instantons on $R4/Z2$ and algebras like $b
gl(2)_2 × NSR$. This conjecture is confirmed by checking the coincidence
of number of fixed points on such instanton moduli space with given
instanton number $N$ and dimension of subspace degree $N$
in the representation of such algebra.
Colomo Filippo
Arctic curves of the six-vertex model
Some two-dimensional models of dimers ant tilings are known to exhibit
spatial phase segregation, with ordered and disordered regions sharply
separated by smooth curves (Arctic curves). Recently, the calculation
of Arctic curves and limit shapes, and the characterization of their
fluctuations has been performed for several such models, with deep
implications in algebraic geometry and algebraic combinatorics. Note
that, even if highly non-trivial, these are all models of discrete free
fermions. In the case of a square lattice, their most natural
generalization incorporating an interaction and preserving integrability
is provided by the six-vertex model.
We here derive the exact form of the Artic curve of the six-vertex model
with domain wall boundary conditions, for the whole phase diagram of
the model. We also discuss the extension of the above result to the
case of the six-vertex model on generic regions of the square lattice
(albeit with suitably chosen boundary conditions).
Doyon Benjamin
The entanglement entropy in integrable QFT
I will review the works I have done with my collaborators J. Cardy and
O. A. Castro Alvaredo concerning the entanglement entropy (EE) in
integrable quantum field theory (QFT). The EE is a measure of the
quantity of entanglement between complementary sectors of observables in
quantum systems. It is a good measure because it cannot increase under
local unitary transformations or classical communications; but also, it
turns out that it contains a lot of "universal" information about the
quantum state. We have studied it in extended quantum systems near to
critical points, where we looked at entanglement between various spatial
regions in the ground state. Such systems display universality and are
described by QFT models, and we have used the powerful mathematical
structure of integrable QFT in order to extract interesting results. We
showed for instance how to evaluate the EE using branch-point twist
fields and partition functions on branched Riemann surfaces, and deduced
how it is connected to the particle spectrum of the QFT or to the
boundary entropy. I will recall the basics of entanglement entropy, and
review these results and ideas.
Essler Fabian
Quantum Quenches in the Transverse Field Ising Model
I consider the time evolution of observables in the transverse eld Ising chain (TFIC) after a
sudden quench of the magnetic field. I present exact analytical results for the asymptotic time and
distance dependence of one- and two-point correlation functions of the order parameter. These results
are based on two complementary approaches based on asymptotic evaluations of determinants and form-factor
sums. I show that the stationary value of the two-point correlation function is not thermal, but
can be described by a generalized Gibbs ensemble (GGE). The approach to the stationary state can
also be understood in terms of a GGE. Generalizations to particular quenches in other integrable models are discussed.
Fateev Vladimir
AGT Conjecture and Integrability.
We show that Alday, Gaiotto and Tachikawa conjecture is valid for
quiver supersymmetric Gauge Theories and gives the combinatorial
expansion for conformal blocks.
Franchini Fabio
Essential singularity of the entanglement entropy in one-dimension
We study the bipartite entanglement entropy for one-dimensional
systems.
Its qualitative behavior is quite well understood: for gapped systems
the entropy saturates to a finite value, while it diverges
logarithmically as the logarithm of the correlation length as one
approaches a critical, conformal point of phase transition.
Using the example of two integrable models, we argue that close to
non-conformal points the entropy shows a peculiar singular behavior,
characteristic of an essential singularity. At these non-conformal
points the model undergoes a discontinuous transition, with a level
crossing in the ground state and a quadratic excitation spectrum. We
propose the entropy as an efficient tool to determine the discontinuous
or continuous nature of a phase transition also in more complicated
models.
- F. Franchini, A. R. Its, B.-Q. Jin, V. E. Korepin; J. Phys. A: Math.
Theor. 40 (2007) 8467-8478
- F. Franchini, A. R. Its, V. E. Korepin; J. Phys. A: Math. Theor. 41
(2008) 025302
- F. Franchini, E. Ercolessi, S. Evangelisti, F. Ravanini; Phys. Rev. B
83 (2011) 012402
Janik Romuald
On universal parts of OPE coefficients in N=4 SYM
N=4 supersymmetric gauge theory is a conformal field theory, thus the
major part of its dynamics is contained in the spectrum of conformal
weights (anomalous dimensions) and OPE coefficients. Currently the
former are very well understood while the latter remain largely unknown.
In this talk I will report on the computation at strong coupling of the
AdS contribution to the 3-point correlation function of operators
corresponding to classical strings which rotate in the S5. This
contribution to the OPE coefficient is universal for all operators which
have only SO(6) charges.
Jimbo Michio
Fermionic basis of local operators in the sine-Gordon model
In this talk we give a survey of recent activities concerning
the structure of the space of local fields in the sine-Gorodn model.
We introduce certain fermions acting on local fields, and explain that
they provide a natural description of one-point functions and form
factors of the descendant fields. This is a joint work with H.Boos, T.
Miwa and F.Smirnov.
Kazakov Vladimir
Solving the AdS/CFT Y-system
I will explain how to transform the infinite AdS/CFT Y-system
calculating the exact spectrum of planar N=4 SYM into a finite set of
non-linear integral equations.
Rim Chaiho
Boundary Matrix model and Liouville Gravity
We present recent progress how to describe 2 dimensional quantum gravity when coupled to minimal matter on disk.
Two descriptions are compared: Liouville gravity and matrix model.
Serban Didina
Conformal blocks and the Calogero-Sutherland model
Conformal blocks of degenerate fields in 2d conformal field theories obey differential equations.
For minimal models, the correlators of the fundamental degenerate fields phi_{12} and phi_{21}
are eigenstates of the Calogero-Sutherland Hamiltonian. This remark allows to retrieve
a natural action of the Calogero-Sutherland integrals of motion on the Hilbert space of the theory,
similar to that found by Alba, Fateev, Litvinov and Tarnopolsky for the Liouville theory
in the context of the AGT conjecture. The same property applies for the WA_{k-1} minimal models.
Tseytlin Arkady
On Pohlmeyer reduced theory for AdS_5 x S5 superstring
We review some features of a gauged WZW model extended by an integrable
potential and fermionic terms that represent Pohlmeyer
reduction of the Green-Schwarz sigma model describing AdS_5 x S5
superstring. The two theories are closely related at the classical level
and may have close connection at the quantum level. We investigate the
structure of the quantum S-matrix for perturbative excitations of the
Pohlmeyer reduced theory. We use as an input the result of the one-loop
perturbative scattering amplitude computation and an analogy with
simpler reduced AdS_n x S^n theories with n=2,3. The n=2 theory is
equivalent to the N=2 2-d supersymmetric sine-Gordon model for which the
exact quantum S-matrix is known. In the n=3 case the one-loop
perturbative S-matrix satisfies the group factorization property and the
Yang-Baxter equation, and reveals the existence of a novel
quantum-deformed 2-d supersymmetry which is not manifest in the action.
The one-loop perturbative S-matrix of the reduced AdS_5 x S5 theory has
the group factorisation property but does not satisfy the Yang-Baxter
equation suggesting some subtlety with the realisation of quantum
integrability. As a possible resolution, we propose that the S-matrix of
this theory may be identified with the quantum-deformed $[psu(2|2)]^2
imes R^2$ symmetric R-matrix constructed in arXiv:1002.1097.
We conjecture the exact all-order form of this S-matrix and discuss
its possible relation to the perturbative S-matrix defined by the path
integral. As in the AdS_3 x S3 case the symmetry of the S-matrix may
be interpreted as an extended quantum-deformed 2-d supersymmetry (see
arXiv:1104.2423 for details).
Wiegmann Pavel
Non-linear waves of the edge of Fractional Hall States (quantum Benjamin-Ono Equation)
xcitations propagating along Fractional Hall Effect Edge are
essentially non-linear. I will show that the simplest Laughlin`s FQHE
state edge excitations are described by a quantum version of a
celebrated Benjamin-Ono equation known in hydrodynamics of stratified
liquids.
I also discuss a relation of quantum Benjamin-Ono equation to the
deformed Conformal Field Theory and emerging Conformal Symmetry in FQHE
states.
Zamolodchikov Alexander
High Energy Scattering in IFT
I will discuss some unsolved problems regarding the Ising Field Theory
(IFT) in a magnetic field. I will report recent progress in analysis of
inelastic cross section and elastic scattering amplitude at high energy.
Titles and abstracts of talks
Bajnok Zoltan
TBA and NLO Luscher corrections in integrably twisted theories
Ground-state energy of integrably twisted theories is analyzed in
finite volume. We derive the leading and next-to-leading order (NLO)
Lüscher type correction of the vacuum for theories with twisted boundary
conditions and twisted S-matrix. Then we derive the twisted
Thermodynamic Bethe Ansatz equations to describe exactly the
ground-state from which we obtain an untwisted Y-system. The two
approaches are compared by expanding the Y-system and/or TBA equations
to NLO. We give explicit results for the O(4) model.
Balog Janos
Mirror TBA equations from Y-system and discontinuity relations
Using the recently proposed set of discontinuity relations we translate
the AdS/CFT Y-system to TBA integral equations and quantization
conditions for a large subset of excited states from the sl(2) sector of
the $AdS_5 imes S^5$ string sigma-model. Our derivation provides an
analytic proof of the fact that the exact Bethe equations reduce to the
Beisert-Staudacher equations in the asymptotic limit. We also construct
the corresponding T-system and show that in the language of T-functions
the energy formula reduces to a single term which depends on a single
T-function.
Belliard Samuel
New ``realisation`` of reflection algebras and some applications.
We will discuss new realisations of the reflection algebras related to
integrables systems with boundaries. By analogy, these new realisations
are equivalent to the q-Serre-Chevalley realisations of the Quantum
groups.
These new realisations have applications in the study of the integrables
systems with boundaries: classification of the integrable (fixed or
dynamical) boundary condition for integrable quantum Toda field theories,
construction of "dynamical" boundary amplitudes for integrable quantum
field theories, non-abelian symmetries of half-infinite spin chains,...
This talk is based on the articles: Baseilhac-Belliard arXiv:0906.1215;
Belliard-Fomin arXiv:1106.1317 and Belliard-Crampe work in progress.
Bombardelli Diego
TBA and double-wrapping corrections for the ground-state of the $gamma_i$-deformed AdS/CFT
We study the finite-size corrections of the $gamma_i$-deformed AdS/CFT
vacuum energy. In particular, we compute the leading (at large volume)
and next-to-leading order (NLO) L"uscher-type corrections, corresponding
to single- and double-wrapping diagrams respectively. On the other
hand, we solve to the NLO the twisted thermodynamic Bethe Ansatz
equations describing exactly the ground-state energy of the theory; then
we compare the results of the two approaches and find exact agreement.
Cantini Luigi
Finite size Emptiness Formation probability for the XXZ spin chain at $Delta=-1/2$
We exploit the relation between the solution of the level $1$
$displaystyle{U_q(hat{sl_2})}$ qKZ equation and the ground state of the
inhomogeneous XXZ spin chain at $Delta=-frac{1}{2}$ in order to compute
the exact Emptiness Formation Probability of a
(twisted-) periodic XXZ spin chain of finite length at
$Delta=-frac{1}{2}$, thus proving the formulae conjectured by
Razumov and Stroganov.
Castro Alvaredo Olalla
Permutation operators and entanglement entropy of quantum spin chains
In this talk I will review a recent new approach to the investigation
of the bi-partite entanglement entropy in integrable quantum spin
chains. Our method employs the well-known replica trick, thus taking a
replica version of the spin chain model as starting point. At each site i
of this new model we construct an operator T_i which acts as a cyclic
permutation among the n replicas of the model. Infinite products of T_i
give rise to local operators, precursors of branch-point twist fields of
quantum field theory. The entanglement entropy is then expressed in
terms of correlation functions of such operators. Employing this
approach we investigate the von Neumann and Renyi entropies of the
ferromagnetic XXX chain. We find that, for large sizes, the entropy
scales logarithmically, but not conformally. We argue that this
behaviour is a direct consequence of the infinite degeneracy of the
ground state.
De Luca Andrea
On the structure of typical states of a disordered Richardson model and many-body localization
We present a thorough numerical study of the Richardson model with
quenched disorder (a fully-connected XX-model with longitudinal random
fields). We study the onset of delocalization in typical states
(many-body delocalization) and the delocalized phase which extends over
the whole range of coupling strength in the thermodynamic limit. We find
a relation between the inverse participation ratio, the
Edwards-Anderson order parameter and the average Hamming distance
between spin configurations covered by a typical eigenstate for which we
conjecture a remarkably simple form for the thermodynamic limit. We
also studied the random process defined by the spread of a typical
eigenstate on configuration space, highlighting several similarities
with hopping on percolated hypercube, a process used to mimic the slow
relaxation of spin glasses.
Doikou Anastasia
Integrable defects: an algebraic approach
The discrete non-linear Schrodinger (NLS) model in the presence of an
integrable defect is examined. The problem is viewed from a purely
algebraic point of view, starting from the fundamental algebraic
relations that rule the model. The first charges in involution are
explicitly constructed, as well as the corresponding Lax pairs. A first
glimpse regarding the corresponding continuum limit is also provided.
Forini Valentina
Generalized quark-antiquark potential at weak and at strong coupling
We study a two--parameter family of Wilson loop operators in
$mathcal{N}=4$ supersymmetric Yang-Mills theory which interpolates
smoothly between the $1/2$ BPS line or circle and a pair of
antiparallel lines. These observables capture a natural generalization
of the quark-antiquark potential. We calculate these loops on the gauge
theory side to
second order in perturbation theory and in a semi--classical expansion
in string theory
to one--loop order. We comment about the feasibility of deriving
all--loop results for these Wilson loops.
Hegedus Arpad
Towards the NLIE formulation of the AdS/CFT spectral problem
According to our present knowledge the NLIE formulation of the
AdS/CFT spectral problem requires the understanding and of the
analyticity properties of the T- and Q-functiuons of the whole
nested hierarchy of the T-hook as well as some quasi local
formulation of the TBA equations.
In this talk we review the construction and the analyticity
properties of the T-functions and show how to formulate the
mirror TBA in a quasi local form.
The talk is based on the e-prints: [arXiv:1104.4054 [hep-th]] and [arXiv:1106.2100 [hep-th]].
Kamenshchik Alexander
General exact solution in a cosmological model based on a
Liouville-like scalar field
We study in
detail the general solution for a scalar field cosmology with an
exponential potential, correcting some imprecisions, encountered
previously in the literature. In addition, we generalize this solution
for a piecewise exponential potential, which is continuous, but not
smooth (with cusps). The main results are presented in the paper
A.A. Andrianov, F. Cannata, A.Yu. Kamenshchik,
General solution of scalar field cosmology with a (piecewise)
exponential potential, arXiv: 1105.4515 [gr-qc]
Levi Emanuele
On a new c-theorem involving branch point twist fields
In this talk I will give evidence that a different function, with
exactly the same qualitative features as Zamolodchikov c-function, may
be defined in terms of the two-point function between a branch point
twist field and the trace of the stress-energy tensor.
Pearce Paul
Coset graphs in logarithmic minimal models
In the boundary theory, multiplication in the Grothendieck ring of
W-projective representations leads to a Verlinde-like formula involving
A-type twisted affine graphs and their coset graphs. This provides
compact formulas for the conformal partition functions with W-projective
boundary conditions. On the torus, modular invariant partition
functions are proposed as sesquilinear forms in W-projective and
rational minimal characters that are encoded by the same coset fusion
graphs.
P.A. Pearce and R. Rasmussen, Nuclear Physics B 846 [FS] (2011) 616–649
Pozsgay Balazs
Local correlations in the 1D Bose gas from a scaling limit of the XXZ chain
A multiple integral formula is presented for the local K-body
correlators of the 1D Bose gas. The result applies for every K and
arbitrary states of the system with a smooth distribution of Bethe
roots, including the ground state and finite temperature Gibbs-states.
In the cases K<=4 we perform the explicit factorization of the
multiple integral.
Rasmussen Jorgen
Boundary conditions and Kac representations in logarithmic minimal models
In the lattice approach to the logarithmic minimal model ${cal
LM}(p,p^{prime})$, one can construct an infinite family of Yang-Baxter integrable
boundary conditions whose continuum scaling limits give rise to
representations of the Virasoro algebra. After introducing their lattice
construction, we will discuss the module structure and fusion properties
of these so-called Kac representations. We will then indicate how another
class of boundary conditions in the same lattice model is associated with
representations of a ${cal W}$-algebra. Their fusion rules are inferred
from the fusion algebra generated by the Kac representations in the
underlying Virasoro picture.
Ratti Carloalberto
Wrapping corrections beyond the sl(2) sector in N=4 SYM
The sl(2) sector of N = 4 SYM has been much studied and the anomalous
dimensions of those operators is well known. Nevertheless, many
interesting operators are not included in this sector. We consider spin
N, length-3, twist operators beyond the sl(2) subsector. They can be
identified at one-loop with three gluon operators. At strong coupling,
they are associated with spinning strings with two spins in AdS space .
We exploit the Y-system to compute the leading weak-coupling four loop
wrapping correction to their anomalous dimension. The result is written
in closed form as a function of the spin N . We combine the wrapping
correction with the known four-loop asymptotic Bethe Ansatz
contribution and analyze special limits in the spin N. In particular, at
large N , we prove that a generalized Gribov-Lipatov reciprocity holds.
Ridout David
Lattice Discretisations of Integrable Sigma Models
A general formalism is proposed for solving a certain class of quantum
integrable sigma models. This involves two steps: First, the quantum
algebra underlying the integrable symmetry of the model is deduced.
Second, this algebra is used to construct R-matrices, L-matrices, etc...
In the important case when the target space is non-compact, the second
step can be carried out on a lattice yielding an integrable
discretisation of the sigma model. This regularises the divergences
that arise in the continuum whilst preserving the quantum symmetries.
The usual methods can then be brought to bear on the lattice model.
Joint work with J"{o}rg Teschner. extsf{arXiv:1102.5716 [hep-th]}
Rossi Marco
The non linear integral equation in the sl(2) sector of N=4 SYM
The non linear integral equation is an important tool especially in
order to compute finite size corrections. I will review recent
applications to the Bethe Ansatz equations which determine anomalous
dimensions in the sl(2) sector of N=4 SYM. In the large (Lorentz) spin
limit the length scale is given by the logarithm of the spin: using the
non linear integral equation finite size corrections are
systematically computed in various regimes. The talk is intended as a
review on results contained in arXiv 0802.0027, 0804.2893, 0808.1886,
0901.3147, 0901.3161, 0911.2425, 1004.1081.
Sasaki Ryu
Exactly solvable quantum mechanics and infinite families of multi
-indexed orthogonal polynomials
Infinite families of multi-indexed orthogonal polynomials are
discovered as the solutions of exactly solvable one-dimensional quantum
mechanical systems. The simplest examples, the one-indexed orthogonal
polynomials, are the infinite families of the exceptional Laguerre
and Jacobi polynomials of type I and II constructed by the present
authors.
The totality of the integer indices of the new polynomials are finite
and they correspond to the degrees of the "virtual state
wavefunctions" which are "deleted" by the generalisation of Crum-Adler
theorem. Each polynomial has another integer $n$ which counts the nodes.
Satoh Yuji
Thermodynamic Bethe ansatz and analytic expansions of gluon scattering amplitudes at strong coupling
We discuss gluon scattering amplitudes of ${Ľcal N}=4$ SYM at strong
coupling by using the thermodynamic Bethe ansatz associated with the
homogeneous sine-Gordon model and conformal perturbation theory. For the
amplitudes corresponding to the minimal surfaces in $AdS_3$, we show
that they are concisely expressed in terms of the T-function. An
interesting relation between the T-function and the g-function (boundary
entropy) then enables us to derive analytic expansions of the
amplitudes around kinematic points of equal cross-ratios of momenta. We
also find that appropriately rescaled remainder functions are very close
to those at weak coupling. [References: Y. Hatsuda, K. Ito, K. Sakai
and Y. Satoh, JHEP 1004(2010)108; 1009(2010)064; 1104(2011)100, and in
preparation.]
Suchanek Paulina
Modular bootstrap in Liouville field theory
I will present a proof of the modular invariance of 1-point functions
on a torus in Liouville field theory with DOZZ structure constants [1].
The proof is based on a relation between the 1-point functions on a
torus and special 4-point functions on a sphere first proposed by
Fateev, Litvinov, Neveu and Onofri [2]. I will show how to derive an
equivalence between 1-point conformal blocks on a torus and a class of
4-point conformal blocks on a sphere [3,4] which together with some
properties of DOZZ structure constants lead to the FLNO relation between
the Liouville correlators.
[1] L. Hadasz, Z. Jaskolski, P. Suchanek, "Modular bootstrap in
Liouville field theory", Phys.Lett.B685:79-85,2010, [arXiv:0911.4296v1
[hep-th]],
[2] V.A. Fateev, A.V. Litvinov, A. Neveu, E. Onofri, "Differential
equation for four-point correlation function in Liouville field theory
and elliptic four-point conformal blocks", J.Phys.A42:304011,2009,
[arXiv:0902.1331],
[3] R. Poghossian "Recursion relations in CFT and N=2 SYM theory", JHEP
0912:038,2009, [arXiv:0909.3412],
[4] L. Hadasz, Z. Jaskolski, P. Suchanek, "Recursive representation of
the torus 1-point conformal block", JHEP 1001(2010)063,
[arXiv:0911.2353]
Takács Gábor
Thermal correlators in integrable models
I review a novel, systematic large-distance/low-temperature expansion
for finite temperature two-point functions, based on a recently
developed formalism for finite volume form factors in integrable models.
Reference: B. Pozsgay and G. Takács, J. Stat. Mech (2010) P11012, arXiv:
1008.3810 [hep-th].
Viti Jacopo
Universal properties of two dimensional percolation
In this talk, I will consider the problem of the determination of the
universal critical amplitude ratios for two-dimensional percolation,
exploiting the integrability of the q-color Potts field theory in the
peculiar $q
ightarrow 1$ limit. I will also discuss the computation of the
three-point connectivity at criticality.
Posters
Evangelisti Stefano
Essential Singularity in the Renyi Entanglement Entropy of the 1d XYZ spin-1/2 chain
We study the Renyi entropy of the 1-d XYZ spin-1/2 chain in the
entirety of its phase diagram. The model has several quantum critical
lines corresponding to rotated XXZ chains in their paramagnetic phase,
and four tri-critical points where these phases join.
Two of these points are described by a conformal FT and close to them
the entropy scales as the logarithm of its mass gap (BKT PT).
The other two points are not conformal and the entropy has a peculiar
singular behavior in their neighbors, characteristic of an essential
singularity (First order PT). Depending on the approach to these points,
the entropy can take any positive value from 0 to ‡. We propose the
entropy as an efficient tool to determine the nature of a PT
Matsui Chihiro
Boundary bound states of spin-1 XXZ/supersymmetric sine-Gordon model
We study the boundary spectrum of the spin-1 XXZ chain through
algebraic Bethe Ansatz both in the homogeneous case and in the strongly
inhomogeneous limit. We compare the results with the boundary
excitations of the supersymmetric sine-Gordon field theory.
Sotiriadis Spyros
Symmetry generators of the Zamolodchikov-Faddeev algebra and their application to quantum quenches in integrable field theories
Motivated by the study of quantum quenches in integrable field theories
(IFTs) and in particular the structure of the initial state after such a
quench, we are led to the investigation of transformations that leave
the Zamolodchikov-Faddeev algebra (i.e. the commutation algebra of the
quasiparticle creation-annihilation operators in an IFT) invariant.
After showing that, unlike in free theories, linear transformations
(Bogoliubov transformations) are not symmetries of the ZF algebra, we
explore simple cases of infinitesimal transformations that do satisfy
the required conditions and study their properties. Applications to
typical IFTs like the Lieb-Liniger and Sinh-Gordon models are also
presented.
Taddia Luca
Estimating Quasi-Long-Range Order Via Rčnyi Entropies
We show how entanglement entropies allow for the estimation of
quasi-long-range order in one dimensional systems whose low-energy
physics is well captured by the Tomonaga-Luttinger liquid universality
class. First, we check our procedure in the exactly solvable XXZ
spin-1/2 chain in its entire critical region, finding very good
agreement with Bethe ansatz results. Then, we show how phase transitions
between different dominant orders may be efficiently estimated by
considering the superfluid-charge density wave transition in a system of
one-dimensional dipolar bosons. Finally, we discuss the application of
this method to multispecies systems such as the one-dimensional Hubbard
model.