My main field of research is
non-perturbative Quantum Field
Theory, with particular emphasys on the integrable and
conformal methods. . In the years, I have contributed to the
follwing fields:
- Conformal Field Theory
- Integrable Models: Quantum inverse scattering, Algebraic and
Thermodynamic Bethe ansatz, finite size effects and NLIE
(non-linear integral equations)
- Lattice Field Theories (1982-86)
Present interests
- Finite size effects in integrable field theories - The
exact approach to finite volume effects in 2D quantum field
theories through NLIE's deducible from Bethe Ansatz has revealed to
be one of the most effective ways to investigate the structure of
energy levels.
- Entanglemet Entropy in conformal and integrable theories
- This fascinating and subtly conceptual subject finds applications
in many areas ranging from information theory to condensed matter
physics, to the physics of evaporation of black holes.
- Non-equilibrium physics and Generalised Hydrodynamics - This relatively new and challenging subject is a realm where integrability is necessary to explain some phenomena of steady states and non-thermalisation in systems that can also observed experimentally thanks to the recent technological progresses in ultracold atom physics.
- Finite size and boundary effects in integrable theories
- These effects find applications ranging from the theory of
strongly correlated electrons in condensed matter physics to the
world-sheet dynamics of strings propagating on curved spaces. They
are governed by non-linear integral equations (NLIE). Here we
illustrate the main results obtained and the ongoing projects on
this topic:
- sine-Gordon - sinh-Gordon through analytic continuation
- the goal of this ongoing project is the reconstruction of the
scaling functions governing the finite size effects in the
sinh-Gordon integrable model as analytic continuation of a subset
of those present in the sine-Gordon model. The delicate mechanisms
leading to the disappearance of some states (solitons and higher
bound states) allow to foresee the roadmap towards extension of
these results to models of great physical relevance, like e.g.
sigma models on non-compact spaces, crucial in the understanding of
the AdS/CFT correspondence.
- NLIE for integrable deformations of sigma-models - at
the quantum level, many integrable sigma models allow for some
deformations of the parameter of the target space in such a way to
stay integrable. The prototypical example is the so called sausage
model, a deformation of the O(3) sigma-model. The goal is to deepen
the integrability of such class of models though the NLIE
(non-linear integral equation) approach.
- Entanglement Entropy (EE) in conformal and integrable
systems - This subject, that has undergone a dramatic increase
of interest after the appearance of a fundamental paper by Cardy
and Calabrese, presents delicate questions on finite size and
boundary effects, as well as stimulating applications to black hole
physics.
- Exact entanglement entropy of the XYZ model and its
sine-Gordon limit - The exact expression for the Von Neumann
entropy for an infinite bipartition of the XYZ spin ½ model has
been obtained, by connecting its reduced density matrix to the
corner transfer matrix of the eight vertex model. Then, the
anisotropic scaling limit of the XYZ chain has been considered,
yielding the 1+1 dimensional sine-Gordon model. The formula for the
entanglement entropy of the latter has the structure of a dominant
logarithmic term plus a constant, in agreement with what is
generally expected for a massive quantum field theory. [1]
- Essential singular behaviour in entanglement entropy of the
XYZ spin chian [2] - The Renyi
entropy of the one-dimensional XYZ spin-1/2 chain in the entirety
of its phase diagram is explored. 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 field theory
and close to them the entropy scales as the logarithm of its mass
gap. The other two points are not conformal and the entropy has a
peculiar singular behavior in their neighbors, 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. The entanglement
entropy is proposed as an efficient tool to determine the
discontinuous or continuous nature of a phase transition also in
more complicated models.
- Correlation Length and Unusual Corrections to the
Entanglement Entropy [3] - We study
analytically the corrections to the leading terms in the Renyi
entropy of a massive lattice theory, showing significant deviations
from naive expectations. In particular, we show that finite size
and finite mass effects give rise to different contributions (with
different exponents) and thus violate a simple scaling argument. In
the specific, we look at the entanglement entropy of a bipartite
XYZ spin-1/2 chain in its ground state. When the system is divided
into two semi-infinite half-chains, we have an analytical
expression of the Renyi entropy as a function of a single mass
parameter. In the scaling limit, we show that the entropy as a
function of the correlation length formally coincides with that of
a bulk Ising model. This should be compared with the fact that, at
criticality, the model is described by a c=1 Conformal Field Theory
and the corrections to the entropy due to finite size effects show
exponents depending on the compactification radius of the theory.
We will argue that there is no contradiction between these
statements. If the lattice spacing is retained finite, the relation
between the mass parameter and the correlation length generates new
subleading terms in the entropy, whose form is path-dependent in
phase-space and whose interpretation within a field theory is not
available yet. These contributions arise as a consequence of the
existence of stable bound states and are thus a distinctive feature
of truly interacting theories, such as the XYZ chain.
