Ground states, symmetries and dynamics of quantum many-body lattice systems

Projektinformationen

QUANTLATTICE

ID Finanzhilfevereinbarung: 101023822

DOI

10.3030/101023822

Das Projekt endete am 30 November 2022

EK-Unterschriftsdatum 14 April 2021

Startdatum 1 August 2021

Enddatum 1 März 2024

Finanziert unter

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Gesamtkosten

€ 207 312,00

EU-Beitrag

€ 207 312,00

Koordiniert durch

KOBENHAVNS UNIVERSITET
Denmark

Periodic Reporting for period 1 - QUANTLATTICE (Ground states, symmetries and dynamics of quantum many-body lattice systems)

Berichtszeitraum: 2021-08-01 bis 2023-07-31

Zusammenfassung vom Kontext und den Gesamtzielen des Projekts

Quantum technology has the potential to revolutionize all aspects of computation and communication. The societal impact would be broad in scope, given that, for example, computing devices and Internet applications are ubiquitous in everyday life, all around the world. Quantum devices would also offer new insights into the basic sciences, accelerating our understanding of physics, chemistry and biology. Realizing this potential will require scientific achievements in both implementation and theory.

Increasingly mature schemes for quantum computation require better understanding of the relevant physical objects. One such object is the quantum mechanical state, which is a probabilistic description of possible outcomes of a quantum system. A special type of state is called the ground state, describing the lowest energy configuration of a system. Ground states have long been identified to play a special role in both statistical mechanics and quantum computing theory. In this project, we investigated properties of ground states, proving new results about their organization and structure. We focused on systems which fit onto a flat plane, the natural setting of quantum computation, with an overall objective of proving mathematical statements about stable properties of their ground states.

Arbeit, die ab Beginn des Projekts bis zum Ende des durch den Bericht erfassten Berichtszeitraums geleistet wurde, und die wichtigsten bis dahin erzielten Ergebnisse

During this project, we demonstrated a rigorous proof of a stable gapped phase of ground states for a non-commuting, two-dimensional many-body Hamiltonian. Our results apply to the decorated Affleck-Kennedy-Lieb-Tasaki models. These models are characterized by the presence of two species of spins arranged on a lattice, such as the hexagonal lattice. The outcome of our work is, to the best of our knowledge, the first of its kind and strengthens our understanding of how quantum systems react to perturbations such as noise.

Fortschritte, die über den aktuellen Stand der Technik hinausgehen und voraussichtliche potenzielle Auswirkungen (einschließlich der bis dato erzielten sozioökonomischen Auswirkungen und weiter gefassten gesellschaftlichen Auswirkungen des Projekts)

Our results extend state of the art knowledge about decorated Affleck-Kennedy-Lieb-Tasaki ground states, leaving open the possibility of continued analysis to potentially bridge gaps between statistical mechanical models and quantum computation.

The decorated Affleck-Kennedy-Lieb-Tasaki model on a hexagonal lattice.