Abstract
Critical phenomena involve structural changes in the correlations of its constituents. Such changes can be reproduced and characterized in quantum simulators able to tackle medium-to-large-size systems. We demonstrate these concepts by engineering the ground state of a three-spin Ising ring by using a pair of entangled photons. The effect of a simulated magnetic field, leading to a critical modification of the correlations within the ring, is analysed by studying two- and three-spin entanglement. In particular, we connect the violation of a multipartite Bell inequality with the amount of tripartite entanglement in our ring.
Highlights
Critical phenomena involve structural changes in the correlations of its constituents
We show that the Svetlichny function evaluated using the simulated ground state of the Ising chain violates the Nparty local-realistic bound that, even for a short chain, is very close to the quantum critical point defined in the thermodynamic limit N R ‘
The bipartite non-locality (Fig. 2 a), which is null for b R 0 and b R 2‘, reaches a non-zero value close to the point of structural changes b^{1, which would correspond to the critical point for N At the same time, the tripartite non-locality witnessed by
Summary
Critical phenomena involve structural changes in the correlations of its constituents. Anyonic statistics[13] and frustration in a Heisenberg chain[14] have been studied in analog photonic quantum simulators, while special topologically protected bound states predicted by models of condensed-matter physics have been emulated[15,16]. One can take the approach of constructing multi-photon states enjoying the same symmetries as the ground states by using continuously tuneable quantum gates realized by means of pre-available entangled pairs of particles and measurement-induced interactions, when necessary[14,16] This approach is relevant when obtaining statistical information by classical computation might be challenging, e.g. the spin correlation function of a one-dimensional antiferromagnetic Heisenberg model[17,18]. In this paper we follow such an approach to demonstrate the nonlocal properties of the ground state of a paradigmatic many-body system: the transverse Ising model
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