Joint research project

Strongly interacting systems in confined geometries

Project leaders
Andrea Trombettoni, Istvan Nandori
Agreement
UNGHERIA - HAS (MTA) - Accademia Ungherese delle Scienze
Call
CNR/HAS triennio 2019-2021 2019-2021
Department
Physical sciences and technologies of matter
Thematic area
Physical sciences and technologies of matter
Status of the project
New

Research proposal

The importance of strongly correlated systems in modern physics can be hardly underestimated. Since in low dimensions and confined geometries the effect of quantum fluctuations is typically stronger than in conventional 3D systems, a challenging - and relevant for experiment applications - task is to study equilibrium and dynamical properties of strongly correlated systems in low dimensional geometries such as 1D waveguides, nanowires, 2D films and optical traps for ultracold atoms. In the last decades powerful tools such as conformal field theory, bootstrap, integrability and renormalization group (RG) have been developed to reckon with the non-trivial effects of strong interactions in low dimensions (1D and 2D). These results provide the premise for a systematic study of a variety of 2D models using the common language of statistical field theory and pave the way to attacking the problem of the study of their properties when they are perturbed or coupled. As typical examples we may mention the dynamical response of a quantum 1D system when subjected to a perturbation like a quantum quench, the effect of integrability breaking terms and the determination of equilibrium and dynamical properties of coupled sine-Gordon models or coupled spin chains.
Given the importance of such strongly correlated systems and their paradigmatic role in understanding quantum many-body properties induced by the interactions, a systematic study of strongly correlated low dimensional systems when perturbed or coupled is a topic of paramount importance. Another reason for such study is that controllable perturbations (as quantum quenches) in low dimensional systems as well as couplings among them are realizable with current-day technology in experiments with cold atoms, low dimensional electron systems and spin chains.
The Italian team foresees the participation of 2 CNR permanent researches (Andrea Trombettoni and Augusto Smerzi), 1 CNR associate (Luca Salasnich)and one SISSA PhD Student (Marton Mestyan). Moreover the Italian team will work on the topics of the project in close collaboration with G. Mussardo and P. Calabrese, who are two internationally recognized well-known experts in the field. The Hungarian team foresees the participation of Istvan Nandori, Tamas Kovacs and Istvan Gabor Marian (Debrecen) and Marton Kormos and Balazs Pozsgay (Budapest), working in collaboration with G. Takacs (Budapest), a leading expert in integrable field theories, and U. Jentschura (Debrecen). All these scientists already agreed to collaborate on the specific topics of the proposal.
The Italian and Hungarian teams have a more-than-one-decade story of continuing and successful collaborations. In particular, several young Hungarian physicists came from Budapest to Trieste to do the Ph.D. or as postdocs working on the subject of low dimensional strongly correlated systems. As examples relevant for this proposal, Marton Kormos worked as a postdoc in Trieste with G. Mussardo and then with P. Calabrese, while Marton Mestyan is currently a Ph.D. student at SISSA under the supervision of P. Calabrese. The Italian-Hungarian scientific connections were tightened by the CNR-MTA project 2012-2015 "Non-perturbative field theory and strongly correlated systems". This project finished in December 2015 and it was motivated by the long-lasting collaboration between the Trieste group and the Hungarian groups in Budapest and Debrecen. The project turned out to be very successful: 9 papers on the subject of strongly correlated systems treated non-perturbatively and resulting from the Italian-Hungarian collaboration were published in international journals within the project, with a total of more than 150 day of visits in Italy and Hungary and 10 talks presented at international conferences.
From the bibliometric point of view, only referring to the last decade, more than 30 papers has been published with authors from Trieste and Budapest/Debrecen involved in the project. For reason of space restrictions we cannot quote them, but the Referees can find the list in the webpage
https://people.sissa.it/~andreatr/Trieste_Budapest_Debrecen_collaboration/
It is fair to say that the Trieste-Budapest/Debrecen collaboration is one of the most scientifically productive Italian-Hungarian collaborations currently active, and that it represents at international level a recognized nucleus of activity in the field of strongly correlated systems in low-dimensions and integrable field theories.
These premises show the expertise of the groups in the development of the theoretical framework to treat challenging low dimensional interacting systems such as interacting quantum bosons and fermions, quantum spin chains and the sine-Gordon model. However, if this was the past, the field of strongly interacting systems in reduced geometries poses continuously new theoretical challenges in view of physical applications, motivated by progress in the manipulation of low-dimensional systems in quantum optics and condensed matter systems, such as cold atoms.
In the present project we individuate four objectives which are at the forefront of actual research: dynamical confinement, quantum quenches, two-dimensional systems and effect of coupling between tw-dimensional systems. The Italy-Hungary teams can study them with their consolidated expertise in RG techniques, conformal field theory, integrable field theory, form factors and out equilibrium dynamics.
Finally, we mention that a key part of the project is the scientific growth of the young researchers (

Research goals

Obj.1 Dynamical confinement: In a recent Nature Physics paper, our collaboration of researchers demonstrated the dramatic effect of confinement on the light cone propagation of entanglement and correlations. We plan to study coupled antiferromagnetic XXZ spin chains where the confinement is triggered by the interaction between the chains.

Obj.2 Study of integrable quenches: We aim at studying integrable quenches with the main goals of obtaining exact overlap formulas and exact solutions for the quenches in higher rank spin chains and the continuum Yang-Gaudin model and obtain exact predictions for quenches in these models.

Obj.3 RG study of sine-Gordon-type models: To model superfluid properties of 2D systems, we will study different classes of models interpolating between the sine- and the sinh-Gordon theories, determining their phase structure. Collaboration with A. Smerzi and T. Kovacs's groups is expected to be crucial to study the effect of the compactness of the phase variable.

Obj.4 Coupled XY models: The properties of (even integrable) systems may drastically change when they are coupled. We plan to study coupled sine-Gordon and coupled XY models with ultracold atoms, by RG, bosonization and lattice Monte Carlo techniques. The main goal of this point 4 is to construct a field theory description of coupled, layered XY models relevant for superconducting and ultracold systems. On this point is foreseen the collaboration with L. Salasnich.

Last update: 24/10/2020