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Published January 2004 | Submitted
Journal Article Open

Ground state entanglement in quantum spin chains

Abstract

A microscopic calculation of ground state entanglement for the XY and Heisenberg models shows the emergence of universal scaling behavior at quantum phase transitions. Entanglement is thus controlled by conformal symmetry. Away from the critical point, entanglement gets saturated by a mass scale. Results borrowed from conformal field theory imply irreversibility of entanglement loss along renormalization group trajectories. Entanglement does not saturate in higher dimensions which appears to limit the success of the density matrix renormalization group technique. A possible connection between majorization and renormalization group irreversibility emerges from our numerical analysis.

Additional Information

© 2004 Rinton Press. Received July 10, 2003; Revised January 13, 2004. We thank A. Kitaev for very valuable input and R. Emparan for fruitful discussions. This work was supported by Spanish grants GC2001SGR-00065 and MCYT FPA2001-3598, by the National Science Foundation of USA under grant EIA–0086038, and by the European Union under grant ISF1999-11053.

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