During the duration of the fellowship the researcher focused on the study of both
equilibrium and out-of-equilibrium entangled many-body quantum systems.
Together with Professor Pasquale Calabrese, the researcher laid the basis
to describe the out-of-equilibrium behavior of entanglement measures
in integrable models, which are models that can be solved analytically.
For instance, in [1,2], the researcher obtained the first exact results
for the out-of-equilibrium dynamics of the entanglement entropy in
integrable interacting models. In [3,4] the researcher
extended the analysis of [1] to the post-quench dynamics of the
Renyi entropies, which are entanglement measures that
have the remarkable property of being experimentally
accessible with cold atomic gases. In [5] the researcher extended the method of [1]
to inhomogeneous systems. These are out-of-equilibrium experiments where two
one dimensional systems with macroscopically different properties are put
in contact and let to evolve.
The understanding of the early stage (prethermal) regimes of the out-of-equilibrium
dynamics after quantum quenches is an important priority of contemporary
physics. In [6] in collaboration with Maurizio Fagotti (from the Ecole Normale
Superieur in Paris) the researcher uncovered a new mechanism leading to interesting prethermal regimes.
These results have been published in Physics Review Letters (PRL). Another intriguing result at the
interface between equilibrium and out-of-equilibrium entangled systems
is in [7]. In the paper, the researcher presented a new method to calculate
the equilibrium values of entanglement measures by using out-of-equilibrium protocols.
A prominent theme of the research project was the investigation of novel
entanglement witnesses and their behavior in complex quantum many-body
phases of matter. In this respect an important quantity is the so-called
logarithmic negativity. In [8], together with the team at SISSA, the researcher
derived general results for the behavior of the entanglement negativity.
One of the novel and most useful entanglement-based theoretical tools is
the entanglement spectrum. In [9], in collaboration with Erik Tonni at SISSA and
Pasquale Calabrese the researcher investigated the structure of the entanglement
spectrum in systems having non-unique ground states.
All the results were communicated in conferences and workshops in prestigious institutions
worldwide.
References:
[1] V. Alba and P. Calabrese, PNAS 114 (30) 7947 (2017), Entanglement and thermodynamics after a quantum
quench in integrable systems.
[2] V. Alba and Pasquale Calabrese, SciPost Phys. 4, 017 (2018), Entanglement dynamics after quantum
quenches in generic integrable systems.
[3] V. Alba and P. Calabrese, Phys. Rev. B 96, 115421 (2017), Quench action and Renyi entropies in integrable
systems.
[4] V. Alba and P. Calabrese, J. Stat. Mech. (2017) 113105, Renyi entropies after releasing the Neel state in
the XXZ spin chain.
[5] V. Alba, Phys. Rev. B 97,245135 (2018), Entanglement and quantum transport in integrable systems.
[6] V. Alba and M. Fagotti, Phys. Rev. Lett. 119, 010601 (2017), Prethermalization at low temperature: Scent
of a spontaneously broken symmetry.
[7] V. Alba, Phys. Rev. E 95, 062132 (2017), Measuring the Renyi entropies: An out-of-equilibrium protocol
via the Jarzynski equality.
[8] G. Bigan Mbeng,V. Alba, and P. Calabrese, J. Phys. A: Math. Theor. 50, 194001 (2017), Negativity
spectrum in gapped phases of matter.
[9] V. Alba, P. Calabrese, and E. Tonni, J. Phys. A 51 024001 (2018), Entanglement spectrum degeneracy and
Cardy formula in 1+1 dimensional conformal field theories.
