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Network Techniques for Interaction Quenches

Periodic Reporting for period 1 - NET4IQ (Network Techniques for Interaction Quenches)

Reporting period: 2016-10-01 to 2018-09-30

With NET4IQ we focused on the study of the out-of-equilibrium dynamics of closed quantum systems via both analytical techniques and new advanced numerical methods.
We used improved numerical algorithms to address some of the most important open questions regarding the dynamics of 1D integrable and nonintegrable quantum models:
(1) How thermalisation (or generalised thermalisation) occurs at late time.
(2) How to characterise transport phenomena after geometric quantum quenches in integrable models.
(3) How conserved quantities may be encoded into state-of-the-art algorithms.
The importance of our findings is mainly related on having understood the mechanisms which determin/constraint the dynamics governing the spreading of information during the unitary time evolution in quantum 1D systems.
This is mainly at the basis of the manipulation of the quantum coherence and, in the long run, may foundamentally contribute in the improving of quantum computing, and within the framework of the quantum technologies, in the realization of a quantum simulator.
(1) We improved algorithms based on tensor network techniques to manipulate integrable/non-integrable models.
(2) We encode Matrix Product Operator (MPO) representation for hermitian and non-hermitian dynamics.
(3) We developed a brand new analytic approach to describe the large space-time scaling properties of the dynamics in integrable models. We namely
Generalised the usual hydrodynamics in order to take into account all conserved quantities characterising Thermodynamic Bethe Ansatz (TBA) solvable models.
(4) We understood the dynamical-confinement mechanism and extended it into nonhomogeneous situations.
(5) We studied the nonequilibrium properties of the Probability Distribution Functions (PDF) characterising the measurement in quantum mechanics.
The very main result which we achieved at the end of the project, and which goes very much beyond the state of the art, is the brand new GENERALIZED HYDRODYNAMICS we introduced to completely describe the Local Quasy-Stationary Sates (LQSS) in the framework of the Thermodynamic Bethe Ansatz (TBA).
Indeed, NET4IQ has given a foundamental contribution in a series of works related to this studies, starting from the ultimate
publication (https://doi.org/10.1103/PhysRevLett.117.207201) which triggered fresh new energy on research in this field.
Our result has been in the spotlight (see the APS Viewpoint https://physics.aps.org/articles/v9/153) mainly because it is largely unexpected, surprisingly simple and clear, and much more important, very general; it thus opens up new exciting possibilities which range from new mathematical investigations on the structure and generalization of our mathematical solution, to a way to describe new classes of experiment on interacting particles that are out of equilibrium.
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