Entanglement entropy of random quantum critical points in one dimension

Details Entanglement entropy of random quantum critical points in one dimension Entanglement entropy of random quantum critical points in one dimension

2004-06-30

arxiv.org/abs/cond-mat/0406737v1

Phys. Rev. Lett. 93, 260602 (2004)

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 3 figures

Scientific paper

10.1103/PhysRevLett.93.260602

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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