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In this talk, I will present the “link representation formalism” that we introduced in our
recent works [1-2], where we assume entanglement entropy of any bipartition of a quantum state
can be approximated as the sum of certain link strengths connecting internal and external sites. The
representation is useful to unveil the geometry associated with the entanglement structure of a
quantum many-body state which may occasionally differ from the one suggested by the
Hamiltonian of the system. In the cases where the representation is exact, the elements of the link
matrix coincide with the mutual information between pairs of sites. In others, it provides a very
good approximation, and in all the cases it yields a natural entanglement contour which is similar to
previous proposals [3]. We will present examples where the representation is exact and then discuss
several non-exact cases where we can apply certain approximation techniques that include, matrix
product states, free fermionic states, or cases in which contiguous blocks are specially relevant. The
accuracy of the representation for different types of states and partitions will also be discussed.
Finally, we show that the representation helps us in extending the quasi-particle picture useful in
explaining the growth of entanglement entropy of short-range initial states when quenched under
critical Hamiltonian, to the initial states presenting long-range correlations [4-5].
References:
[1] Sudipto Singha Roy, Silvia N. Santalla, Javier Rodríguez-Laguna, and Germán Sierra,
“Entanglement as geometry and flow”, Physical Review B 101, 195134 (2020).
[2] Sudipto Singha Roy, Silvia N.Santalla, Germán Sierra, and Javier Rodríguez-Laguna, “Link
representation of the entanglement entropies for all bipartitions”, Journal of Physics A:
Mathematical and Theoretical 54, 305301 (2021).
[3] Y. Chen and G. Vidal, “Entanglement contour”, J. Stat. Mech. P10011 (2014).
[4] Sudipto Singha Roy, Giovanni Ramírez, Silvia N. Santalla, Germán Sierra, and Javier
Rodríguez-Laguna, “Exotic correlation spread in free-fermionic states with initial patterns”,
Physical Review B 105, 214306 (June 2022).
[5] Silvia N. Santalla, Giovanni Ramírez, Sudipto Singha Roy, Germán Sierra, and Javier
Rodríguez-Laguna , “Entanglement links and the quasiparticle picture”, arXiv:2208.03766 [quant-
ph] (2022). |