An area law for onedimensional quantum systems
Abstract
We prove an area law for the entanglement entropy in gapped onedimensional quantum systems. The bound on the entropy grows surprisingly rapidly with the correlation length; we discuss this in terms of properties of quantum expanders and present a conjecture on matrix product states which may provide an alternate way of arriving at an area law. We also show that, for gapped, local systems, the bound on Von Neumann entropy implies a bound on Rényi entropy for sufficiently large α<1 and implies the ability to approximate the ground state by a matrix product state.
 Publication:

Journal of Statistical Mechanics: Theory and Experiment
 Pub Date:
 August 2007
 DOI:
 10.1088/17425468/2007/08/P08024
 arXiv:
 arXiv:0705.2024
 Bibcode:
 2007JSMTE..08...24H
 Keywords:

 Quantum Physics;
 Condensed Matter  Strongly Correlated Electrons;
 Mathematical Physics
 EPrint:
 9 pages, 1 figure