Düsseldorf 2007 – wissenschaftliches Programm
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Q: Fachverband Quantenoptik und Photonik
Q 18: Quanteninformation (Verschränkung und Dekohärenz I)
Q 18.8: Vortrag
Dienstag, 20. März 2007, 12:30–12:45, 5L
Statistics dependence of the entanglement entropy — •Marcus Cramer1, Jens Eisert2,3, and Martin Plenio2,3 — 1Institut für Physik, Universität Potsdam, Am Neuen Palais 10, D-14469 Potsdam, Germany — 2QOLS, Blacket Laboratory, Imperial College London, Exhibition Road, London, SW7 2BW, UK — 3Institute for Mathematical Sciences, Imperial College London, Exhibition Road, London, SW7 2BW, UK
The entanglement entropy of a distinguished region of a quantum many-body problem reflects the entanglement present in its pure ground state. In this work, we establish scaling laws for the entanglement entropy for critical quasi-free fermionic and bosonic lattice systems, without resorting to numerical means. We consider the geometrical setting of D-dimensional half-spaces. Intriguingly, we find a difference in the scaling properties depending on whether the system is bosonic---where an area-law is first proven to hold---or fermionic, extending previous findings for cubic regions. For bosonic systems with nearest neighbor interaction we prove the conjectured area-law by computing the logarithmic negativity analytically. For fermions we determine the multiplicative logarithmic correction to the area-law, which depends on the topology of the Fermi surface. We find that Lifshitz quantum phase transitions are accompanied with a non-analyticity in the prefactor of the leading order term.