非表示:
キーワード:
High Energy Physics - Theory, hep-th, Condensed Matter, Statistical Mechanics, cond-mat.stat-mech, Condensed Matter, Strongly Correlated Electrons, cond-mat.str-el,Quantum Physics, quant-ph
要旨:
In order to investigate subsystem eigenstate thermalization hypothesis (ETH)
for two-dimensional large central charge conformal field theory, we evaluate
the single-interval R\'enyi entropy and entanglement entropy for a heavy
primary state in short interval expansion. We verify the results of R\'enyi
entropy by three different replica methods. We find nontrivial results at the
eighth order of short interval expansion, which include an infinite number of
higher order terms in the large central charge expansion. We then evaluate the
relative entropy of the reduced density matrices to measure the difference
between the heavy primary state and thermal state, and find that the
aforementioned nontrivial eighth order results make the relative entropy
unsuppressed in the large central charge limit. By Fannes-Audenaert inequality,
these results yield a lower bound on trace distance of the excited state and
thermal state reduced density matrices, which is crucial in checking the
validity of subsystem ETH. We find that whether the subsystem ETH is violated
depends on how the effective dimension of the reduced density matrix scales
with the large central charge. If the effective dimension is strictly infinite,
then it yields no useful information for checking the validity of subsystem
ETH. If the effective dimension scales exponentially with the large central
charge, the trace distance is at most power suppressed, and subsystem ETH would
be violated, while the local ETH remains intact. As a byproduct we also
calculate the relative entropy and distance to measure the difference between
the reduced density matrices of two different heavy primary states.
