2 research outputs found
Real-space entanglement spectrum of quantum Hall systems
We study the real-space entanglement spectrum for fractional quantum Hall
systems, which maintains locality along the spatial cut, and provide evidence
that it possesses a scaling property. We also consider the closely-related
particle entanglement spectrum, and carry out the Schmidt decomposition of the
Laughlin state analytically at large size.Comment: 5 pages, 4 figures. V2: a bit more on non-locality of OP. V3: typos
corrected; as publishe
Entanglement in gapless resonating valence bond states
We study resonating-valence-bond (RVB) states on the square lattice of spins
and of dimers, as well as SU(N)-invariant states that interpolate between the
two. These states are ground states of gapless models, although the
SU(2)-invariant spin RVB state is also believed to be a gapped liquid in its
spinful sector. We show that the gapless behavior in spin and dimer RVB states
is qualitatively similar by studying the R\'enyi entropy for splitting a torus
into two cylinders, We compute this exactly for dimers, showing it behaves
similarly to the familiar one-dimensional log term, although not identically.
We extend the exact computation to an effective theory believed to interpolate
among these states. By numerical calculations for the SU(2) RVB state and its
SU(N)-invariant generalizations, we provide further support for this belief. We
also show how the entanglement entropy behaves qualitatively differently for
different values of the R\'enyi index , with large values of proving a
more sensitive probe here, by virtue of exhibiting a striking even/odd effect.Comment: 44 pages, 14 figures, published versio