Statistics Dependence of the Entanglement Entropy
Abstract
The entanglement entropy of a distinguished region of a quantum manybody system reflects the entanglement in its pure ground state. Here we establish scaling laws for this entanglement in critical quasifree fermionic and bosonic lattice systems, without resorting to numerical means. We consider the setting of Ddimensional halfspaces which allows us to exploit a connection to the onedimensional case. Intriguingly, we find a difference in the scaling properties depending on whether the system is bosonic—where an area law is proven to hold—or fermionic where we determine a logarithmic correction to the area law, which depends on the topology of the Fermi surface. We find Lifshitz quantum phase transitions accompanied with a nonanalyticity in the prefactor of the leading order term.
 Publication:

Physical Review Letters
 Pub Date:
 June 2007
 DOI:
 10.1103/PhysRevLett.98.220603
 arXiv:
 arXiv:quantph/0611264
 Bibcode:
 2007PhRvL..98v0603C
 Keywords:

 05.50.+q;
 03.67.Mn;
 05.30.d;
 05.70.a;
 Lattice theory and statistics;
 Entanglement production characterization and manipulation;
 Quantum statistical mechanics;
 Thermodynamics;
 Quantum Physics;
 Condensed Matter  Other Condensed Matter;
 High Energy Physics  Theory
 EPrint:
 4 pages, 1 figure (essentially identical with published version)