Energy and entanglement in many-body physics
Tuesday, April 19th, 2005Date: April 22, 2005
Who: Mark Dowling
Seminar type: PhD confirmation seminar
Abstract:
In quantum many-body systems entanglement plays an important but poorly-understood role. In recent years there has been much interest in developing new approaches to studying these systems based on the quantitative understanding of entanglement that has emerged from quantum information theory. We begin by explaining the motivation for these approaches and describe some of the early successes, particularly for strongly-correlated systems. We then give an overview of two new approaches to studying entanglement in quantum many-body systems.
In the first we are concerned with systems of distinguishable particles, such as spins on a lattice, where all low-energy states are entangled. We utilise a correspondence between the Hamiltonian and the concept of an entanglement witness from the theory of mixed-state entanglement [1]. For many spin lattices we prove that the difference in energy between the lowest-energy classical configuration and the true ground state necessarily decreases as the coordination number is increased, a result that may be related to mean-field theory. Finally we describe our current work on systems of indistinguishable particles, where the concept of entanglement is much more subtle. Following the work of Wiseman and Vaccaro [2] we define a notion of accessible entanglement; in systems of bosons and fermions, and discuss its relationship to known physics using the Hubbard model as an example.
References:
- [1] Mark R. Dowling, Andrew C. Doherty and Stephen D. Bartlett, Phys. Rev. A 70, 062113 (2004)
- [2] H. M. Wiseman and J. A. Vaccaro, Phys. Rev. Lett. 91, 097902 (2003)