Theory of finite-entanglement scaling at one-dimensional quantum critical points

• Published in: Physical review letters 2009-06, Vol.102 (25), p.255701-255701, Article 255701
• Main Authors: Pollmann, Frank, Mukerjee, Subroto, Turner, Ari M, Moore, Joel E
• Format: Article
• Language: English
• ISSN: 0031-9007; 1079-7114
• DOI: 10.1103/physrevlett.102.255701

Studies of entanglement in many-particle systems suggest that most quantum critical ground states have infinitely more entanglement than noncritical states. Standard algorithms for one-dimensional 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. Finite-entanglement scaling in one-dimensional 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 density-matrix eigenvalues at a critical point [P. Calabrese and A. Lefevre, Phys. Rev. A 78, 032329 (2008)10.1103/PhysRevA.78.032329]. The parameter-free theory is checked against numerical scaling at several quantum critical points.