3 research outputs found
Exact relationship between the entanglement entropies of XY and quantum Ising chains
We consider two prototypical quantum models, the spin-1/2 XY chain and the
quantum Ising chain and study their entanglement entropy, S(l,L), of blocks of
l spins in homogeneous or inhomogeneous systems of length L. By using two
different approaches, free-fermion techniques and perturbational expansion, an
exact relationship between the entropies is revealed. Using this relation we
translate known results between the two models and obtain, among others, the
additive constant of the entropy of the critical homogeneous quantum Ising
chain and the effective central charge of the random XY chain.Comment: 6 page
Entanglement entropy of aperiodic quantum spin chains
We study the entanglement entropy of blocks of contiguous spins in
non-periodic (quasi-periodic or more generally aperiodic) critical Heisenberg,
XX and quantum Ising spin chains, e.g. in Fibonacci chains. For marginal and
relevant aperiodic modulations, the entanglement entropy is found to be a
logarithmic function of the block size with log-periodic oscillations. The
effective central charge, c_eff, defined through the constant in front of the
logarithm may depend on the ratio of couplings and can even exceed the
corresponding value in the homogeneous system. In the strong modulation limit,
the ground state is constructed by a renormalization group method and the
limiting value of c_eff is exactly calculated. Keeping the ratio of the block
size and the system size constant, the entanglement entropy exhibits a scaling
property, however, the corresponding scaling function may be nonanalytic.Comment: 6 pages, 2 figure
Entanglement entropy in aperiodic singlet phases
We study the average entanglement entropy of blocks of contiguous spins in
aperiodic XXZ chains which possess an aperiodic singlet phase at least in a
certain limit of the coupling ratios. In this phase, where the ground state
constructed by a real space renormalization group method, consists
(asymptotically) of independent singlet pairs, the average entanglement entropy
is found to be a piecewise linear function of the block size. The enveloping
curve of this function is growing logarithmically with the block size, with an
effective central charge in front of the logarithm which is characteristic for
the underlying aperiodic sequence. The aperiodic sequence producing the largest
effective central charge is identified, and the latter is found to exceed the
central charge of the corresponding homogeneous model. For marginal aperiodic
modulations, numerical investigations performed for the XX model show a
logarithmic dependence, as well, with an effective central charge varying
continuously with the coupling ratio.Comment: 18 pages, 9 figure