Tensor Network Truncated Conformal Space Approach

Project Information

TNTCSA

Grant agreement ID: 101030988

DOI

10.3030/101030988

Project terminated on 30 September 2022

EC signature date 22 July 2021

Start date 1 October 2021

End date 31 October 2023

Funded under

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Total cost

€ 174 806,40

EU contribution

€ 174 806,40

Coordinated by

FREIE UNIVERSITAET BERLIN
Germany

Periodic Reporting for period 1 - TNTCSA (Tensor Network Truncated Conformal Space Approach)

Reporting period: 2021-10-01 to 2023-09-30

Summary of the context and overall objectives of the project

Ultracold atom experiments study the properties and behaviours of small ensembles of atoms cooled to the lowest temperatures in the universe. This opens a window to fully quantum mechanical motion in systems of many particles, offering the opportunity to experimentally simulate physics problems that are too hard to solve and paving the way to novel technological applications that exploit quantum phenomena. One of the theoretical problems that remains a challenge in this field is the numerical simulation of models of quantum field theory. Quantum field theory is the mathematical framework describing the interactions between elementary particles, and it is also useful in condensed matter and atomic physics. The TNTCSA project has developed a novel numerical technique to simulate out-of-equilibrium dynamics in such models. Moreover, it helped to experimentally demonstrate theoretical predictions of quantum field theory both at equilibrium and out of it.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

Combining two earlier methods, our group at FU Berlin developed a numerical technique to simulate models of quantum field theory. One of these models is the so-called quantum sine-Gordon model, which has important applications in ultracold atom experiments. The new method was able to generate new results for physical characteristics of this model both at equilibrium and out of equilibrium.

Moreover, in collaboration with the “AtomChip” experimental group at TU Wien, we studied two physical properties of matter as seen through ultracold atom experiments. The information needed to fully characterise the state of a system of particles at equilibrium is theoretically expected to be limited according to what is known as “area law”. Using a technique to extract the full information content of an ultracold atom system, we helped to observe this theoretical limit experimentally. On the other hand, when such systems are driven out of equilibrium by some abrupt change, the information of this change propagates through the system at a characteristic speed, as if it was carried by travelling particles. When the density of the atoms varies from point to point, the characteristic speed varies as well. Developing theoretical tools we helped to experimentally observe how the variation of the characteristic speed affects the propagation of information, in analogy to how light trajectories bend in curved spacetime as predicted by the general theory of relativity.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

The new numerical technique that was developed in the framework of this project and applied to the sine-Gordon model, can generate more accurate results and in a more efficient way compared to earlier techniques. This first success opens up the possibility to study also other models of quantum field theory that are currently hard to solve or completely inaccessible by means of numerical methods. Such models include those of Quantum ElectroDynamics and Quantum ChromoDynamics, at least in one space dimension, opening up the possibility of applications to particle physics. The new method has the potential of becoming a standard tool for the study of continuous models, similarly to analogous tools for the study of discrete models.

On the other hand, our work improved our theoretical understanding of ultracold atom experiments and helped demonstrate new capabilities. Experiments performed by the “AtomChip” group are a special type of ultracold atom experiments that use an electronic device, known as the "atom chip", to control and manipulate atoms. Such experiments have demonstrated a potential for simulating the behaviour of quantum fields. The advances in the theoretical description of these experiments made in the framework of the TNTCSA project, not only allowed us to verify important theoretical predictions for the behaviour of quantum fields, but also serve as necessary preliminary steps towards utilising this experimental platform for technological applications.

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