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Published December 31, 2004 | public
Journal Article Open

Entanglement Entropy of Random Quantum Critical Points in One Dimension

Abstract

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.

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.

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August 22, 2023
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October 16, 2023