Corrélations Quantiques & Intrication dans les états Liens de Valence – Q-BONDS

At low temperature, quantum fluctuations in frustrated antiferromagnetic spin systems are strong enough to prevent long range magnetic ordering and generate unconventional and only partially understood states of matter, such as Valence Bond Crystals or Spin Liquids. These states are deep inside the quantum regime and can not be apprehended on semi-classical grounds. Moreover, they provide genuine examples of macroscopic quantum objects characterized by both substantial entanglement and unusual magnetic correlations. In that respect, they lie at a crossing point between modern issues in condensed matter physics and quantum information theory. A simple calculation of the magnetic correlation or von Neumann entropy of the singlet state made out of two spins reveals that it can be seen as the elementary brick to build these correlations and entanglement. Hence, Valence Bond states defined as products of two-spin singlets are ideal tools to understand the exotic physics of frustrated antiferromagnets at low temperature, as well as to study routes to generate massively entangled states. Using new approaches based on Valence Bond states, the aim of the present project is to investigate these unconventional low-energy states emerging from realistic spin or effective dimer models, from both a condensed matter and quantum information perspective. Ultimately, we would like to tackle the question of the interplay between quantum correlations and entanglement. Our young team has a leading expertise in the field of frustrated antiferromagnetism and high precision large-scale simulations. Thanks to recent advances both at numerical and analytical levels for the treatment of Valence Bond states, we expect major breakthroughs in the understanding of the quantum phases emerging in these systems during the next years. On the other hand, our interest for quantum information aspects led us to introduce recently an alternative measurement of bipartite entanglement present in antiferromagnets. In particular, we could characterize entanglement properties of two-dimensional spin systems. This is a major advance as, up to now, essentially only one-dimensional cases were tractable. This successful first step is typical of what we plan to bring to the field of quantum information in the frame of this project and illustrates how efficient condensed matter techniques and concepts can unlock quantum information questions.