27 research outputs found
Quantum entanglement in random physical states
Most states in the Hilbert space are maximally entangled. This fact has
proven useful to investigate - among other things - the foundations of
statistical mechanics. Unfortunately, most states in the Hilbert space of a
quantum many body system are not physically accessible. We define physical
ensembles of states by acting on random factorized states by a circuit of
length k of random and independent unitaries with local support. We study the
typicality of entanglement by means of the purity of the reduced state. We find
that for a time k=O(1) the typical purity obeys the area law. Thus, the upper
bounds for area law are actually saturated {\em in average}, with a variance
that goes to zero for large systems. Similarly, we prove that by means of local
evolution a subsystem of linear dimensions is typically entangled with a
volume law when the time scales with the size of the subsystem. Moreover, we
show that for large values of k the reduced state becomes very close to the
completely mixed state.Comment: updated to published version, typos correcte
Local response of topological order to an external perturbation
We study the behavior of the R\'enyi entropies for the toric code subject to
a variety of different perturbations, by means of 2D density matrix
renormalization group and analytical methods. We find that R\'enyi entropies of
different index {\alpha} display derivatives with opposite sign, as opposed to
typical symmetry breaking states, and can be detected on a very small subsystem
regardless of the correlation length. This phenomenon is due to the presence in
the phase of a point with flat entanglement spectrum, zero correlation length,
and area law for the entanglement entropy. We argue that this kind of splitting
is common to all the phases with a certain group theoretic structure, including
quantum double models, cluster states, and other quantum spin liquids. The fact
that the size of the subsystem does not need to scale with the correlation
length makes it possible for this effect to be accessed experimentally.Comment: updated to published versio