# ProjectAdiLong – Adiabatic driving and linear response in long-range quantum many-body systems

## Basic data

Acronym:

AdiLong

Title:

Adiabatic driving and linear response in long-range quantum many-body systems

Duration:

01/10/2022 to 30/09/2026

Abstract / short description:

Our goal is to develop a rigorous understanding of how the range of interactions and the system size affect the quality of the adiabatic approximation and the validity of linear response theory in quantum spin systems with gapped ground state. To this end, we will construct and analyze non- equilibrium almost-stationary states for perturbations of such systems and their response to adiabatic changes in the Hamiltonian. In particular, we will investigate the extent to which existing results for systems with short-range interactions can be generalized to intermediate- or long-range interactions. The focus will be on sharpening and improving mathematical tools to prove rigorous statements and error estimates. However, another important aspect is that understanding the mathematical obstacles to generalization from short- to long-range will also shed light on the question of which decay exponents can be expected to exhibit qualitatively new behavior with respect to the thermodynamic limit. The answers to these questions are relevant to all areas where adiabatic protocols are applied to many-body systems, to pre-thermalization in many-body systems, and to linear response theory.

Keywords:

Quantum spin systems

Long-range interactions

Adiabatic theory

Linear response

## Involved staff

### Managers

Faculty of Science

University of Tübingen

University of Tübingen

Department of Mathematics

Faculty of Science

Faculty of Science

SFB-TR 352 - Mathematics of Many-Body Quantum Systems and Their Collective Phenomena

Collaborative research centers and transregios

Collaborative research centers and transregios

### Other staff

Department of Mathematics

Faculty of Science

Faculty of Science

## Local organizational units

Department of Mathematics

Faculty of Science

University of Tübingen

University of Tübingen

## Funders

Bonn, Nordrhein-Westfalen, Germany