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Entanglement Entropy of Random Quantum Critical Points in One Dimension

Refael, G. and Moore, J. E. (2004) Entanglement Entropy of Random Quantum Critical Points in One Dimension. Physical Review Letters, 93 (26). Art. No. 260602. ISSN 0031-9007. doi:10.1103/PhysRevLett.93.260602.

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For quantum critical spin chains without disorder, it is known that the entanglement of a segment of N>>1 spins with the remainder is logarithmic in N with a prefactor fixed by the central charge of the associated conformal field theory. We show that for a class of strongly random quantum spin chains, the same logarithmic scaling holds for mean entanglement at criticality and defines a critical entropy equivalent to central charge in the pure case. This effective central charge is obtained for Heisenberg, XX, and quantum Ising chains using an analytic real-space renormalization-group approach believed to be asymptotically exact. For these random chains, the effective universal central charge is characteristic of a universality class and is consistent with a c-theorem.

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Additional Information:©2004 The American Physical Society (Received 29 June 2004; published 21 December 2004) We gratefully acknowledge useful conversations with L. Balents, A. Kitaev, A.W.W. Ludwig, J. Preskill, and G. Vidal, and support from NSF PHY99-07949, DMR-0238760, and the Hellman Foundation.
Subject Keywords:critical points; quantum entanglement; Ising model; Heisenberg model
Issue or Number:26
Record Number:CaltechAUTHORS:REFprl04
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7109
Deposited By: Archive Administrator
Deposited On:09 Jan 2007
Last Modified:08 Nov 2021 20:39

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