Theory of FiniteEntanglement Scaling at OneDimensional Quantum Critical Points
Abstract
Studies of entanglement in manyparticle systems suggest that most quantum critical ground states have infinitely more entanglement than noncritical states. Standard algorithms for onedimensional systems construct model states with limited entanglement, which are a worse approximation to quantum critical states than to others. We give a quantitative theory of previously observed scaling behavior resulting from finite entanglement at quantum criticality. Finiteentanglement scaling in onedimensional systems is governed not by the scaling dimension of an operator but by the "central charge" of the critical point. An important ingredient is the universal distribution of densitymatrix eigenvalues at a critical point [P. Calabrese and A. Lefevre, Phys. Rev. A 78, 032329 (2008)PLRAAN1050294710.1103/PhysRevA.78.032329]. The parameterfree theory is checked against numerical scaling at several quantum critical points.
 Publication:

Physical Review Letters
 Pub Date:
 June 2009
 DOI:
 10.1103/PhysRevLett.102.255701
 arXiv:
 arXiv:0812.2903
 Bibcode:
 2009PhRvL.102y5701P
 Keywords:

 64.70.Tg;
 03.67.Mn;
 75.10.Pq;
 Quantum phase transitions;
 Entanglement production characterization and manipulation;
 Spin chain models;
 Condensed Matter  Strongly Correlated Electrons;
 Quantum Physics
 EPrint:
 4 pages + 2 pages supplementary information