Entanglement Entropy of Random Quantum Critical Points in One Dimension

G. Refael and J. E. Moore
Phys. Rev. Lett. 93, 260602 – Published 21 December 2004

Abstract

For quantum critical spin chains without disorder, it is known that the entanglement of a segment of N1 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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  • Received 29 June 2004

DOI:https://doi.org/10.1103/PhysRevLett.93.260602

©2004 American Physical Society

Authors & Affiliations

G. Refael1 and J. E. Moore2,3

  • 1Kavli Institute of Theoretical Physics, Santa Barbara, California 93106, USA
  • 2Department of Physics, University of California, Berkeley, California 94720, USA
  • 3Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

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Issue

Vol. 93, Iss. 26 — 31 December 2004

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