Entanglement entropy of random quantum critical points in one dimension

TL;DR

This paper demonstrates that strongly random quantum spin chains at criticality exhibit a universal logarithmic entanglement entropy scaling, characterized by an effective central charge similar to the pure case, using an analytic RG approach.

Contribution

It introduces an effective central charge for random quantum critical chains, extending the concept of conformal field theory to disordered systems through an analytic real-space RG method.

Findings

Logarithmic entanglement scaling in random chains at criticality.

Definition of an effective central charge for disordered systems.

Consistency with a c-theorem for the effective central charge.

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.