Monte Carlo Study of Entanglement Scaling in Random S=1/2 Heisenberg Chains

We present the results of a quantum Monte Carlo study of the S=1/2 Heisenberg chain with random antiferromagnetic nearest-neighbor coupling. Using the method of ground state projection in the singlet-bond basis, recently introduced by Sandvik,\footnote{A. Sandvik, PRL {\bf 95}, 207203 (2005).} we are able to directly confirm the expected freezing of the ground state into a random singlet phase at long length scales, while at the same time exactly capturing the nonuniversal (i.e. detail dependent) short-range bond fluctuations. By computing the bond-length distribution in the random singlet phase we are then able to determine the mean entanglement entropy, $S_N$, associated with a segment of $N \gg 1$ spins, both by self-averaging over segments for a particular realization of disorder, and by averaging over many distinct realizations of disorder. Our results confirm the $S_N \simeq \frac{\ln 2}{3} \log_2 N$ scaling found by Refael and Moore using real space RG,\footnote{G. Refael and J. E. Moore, PRL {\bf 93}, 260602 (2004).} showing that the ``effective central charge" of the critical random S=1/2 Heisenberg chain is $\tilde c = \ln 2$. Work supported by US DOE.