A
bstract
We introduce and study generalized Rényi entropies defined through the traces of products of Tr
B
(| Ψ
i
⟩⟨Ψ
j
| ) where ∣Ψ
i
⟩ are eigenstates of a two-dimensional conformal field theory ...(CFT). When ∣Ψ
i
⟩ = ∣Ψ
j
⟩ these objects reduce to the standard Rényi entropies of the eigenstates of the CFT. Exploiting the path integral formalism, we show that the second generalized Rényi entropies are equivalent to four point correlators. We then focus on a free bosonic theory for which the mode expansion of the fields allows us to develop an efficient strategy to compute the second generalized Rényi entropy for all eigenstates. As a byproduct, our approach also leads to new results for the standard Rényi and relative entropies involving arbitrary descendent states of the bosonic CFT.
A
bstract
In this paper, we apply the form factor bootstrap approach to branch point twist fields in the
q
-state Potts model for
q
≤ 3. For
q
= 3 this is an integrable interacting quantum field ...theory with an internal discrete ℤ
3
symmetry and therefore provides an ideal starting point for the investigation of the symmetry resolved entanglement entropies. However, more generally, for
q
≤ 3 the standard Rényi and entanglement entropies are also accessible through the bootstrap programme. In our work we present form factor solutions both for the standard branch point twist field with
q
≤ 3 and for the composite (or symmetry resolved) branch point twist field with
q
= 3. In both cases, the form factor equations are solved for two particles and the solutions are carefully checked via the ∆-sum rule. Using our analytic predictions, we compute the leading finite-size corrections to the entanglement entropy and entanglement equipartition for a single interval in the ground state.
Conformal field theory (CFT) has been extremely successful in describing
large-scale universal effects in one-dimensional (1D) systems at quantum critical points.
Unfortunately, its applicability in ...condensed matter physics has been limited to situations in which the bulk is uniform
because CFT describes low-energy excitations around some energy scale, taken to be constant throughout the system.
However, in many experimental contexts, such as quantum gases in trapping potentials and in several out-of-equilibrium situations,
systems are strongly inhomogeneous.
We show here that the powerful CFT methods can be extended to deal with such 1D situations, providing a few concrete examples
for non-interacting Fermi gases.
The system's inhomogeneity enters the field theory action through parameters that vary with position;
in particular, the metric itself varies, resulting in a CFT in curved space.
This approach allows us to derive exact formulas for entanglement entropies which were not known
by other means.
Multiple Sclerosis (MS) and Rheumatoid Arthritis (RA) are common, chronic, autoimmune diseases affecting many people worldwide. While clinically very different in their phenotype, both diseases are ...thought to have an autoimmune-mediated origin. MS and RA share genetic similarities, and in both diseases, antibodies against host antigens can be found. Aside from the well-known somatic symptoms, many RA patients also show signs and symptoms of psychiatric illnesses, of which depression is the most common diagnosis. In this commentary, both diseases will be introduced and briefly characterized individually and then compared. Depression will be introduced as one of the most frequent psychiatric diseases in the general population. This paper focuses on presenting the possible causes, including psychosocial factors, genetics, and immunologic mechanisms. Hypotheses aimed to explain the higher incidence of depression in these two seemingly different autoimmune diseases will be discussed.
PDF
