Mario Collura, Luca Dell'Anna, Timo Felser, Simone Montangero
SciPost Phys. Core 4, 001 (2021) ·
published 2 February 2021
|
· pdf
In many cases, Neural networks can be mapped into tensor networks with an
exponentially large bond dimension. Here, we compare different sub-classes of
neural network states, with their mapped tensor network counterpart for
studying the ground state of short-range Hamiltonians. We show that when
mapping a neural network, the resulting tensor network is highly constrained
and thus the neural network states do in general not deliver the naive expected
drastic improvement against the state-of-the-art tensor network methods. We
explicitly show this result in two paradigmatic examples, the 1D ferromagnetic
Ising model and the 2D antiferromagnetic Heisenberg model, addressing the lack
of a detailed comparison of the expressiveness of these increasingly popular,
variational ans\"atze.
SciPost Phys. 7, 053 (2019) ·
published 22 October 2019
|
· pdf
We derive some entanglement properties of the ground states of two classes of quantum spin chains described by the Fredkin model, for half-integer spins, and the Motzkin model, for integer ones. Since the ground states of the two models are known analytically, we can calculate the entanglement entropy, the negativity and the quantum mutual information exactly. We show, in particular, that these systems exhibit long-distance entanglement, namely two disjoint regions of the chains remain entangled even when the separation is sent to infinity, i.e. these systems are not affected by decoherence. This strongly entangled behavior, occurring both for colorful versions of the models (with spin larger than 1/2 or 1, respectively) and for colorless cases (spin 1/2 and 1), is consistent with the violation of the cluster decomposition property. Moreover we show that this behavior involves disjoint segments located both at the edges and in the bulk of the chains.
Prof. Dell'Anna: "Dear Editor, I would like ..."
in Submissions | report on Long-distance entanglement in Motzkin and Fredkin spin chains