Quantum Phase Transitions in Anti-ferromagnetic Planar Cubic Lattices

Abstract

Motivated by its relation to an $\mathcal{NP}$-hard problem, we analyze the ground state properties of anti-ferromagnetic Ising-spin networks embedded on planar cubic lattices, under the action of homogeneous transverse and longitudinal magnetic fields. This model exhibits a quantum phase transition at critical values of the magnetic field, which can be identified by the entanglement behavior, as well as by a Majorization analysis. The scaling of the entanglement in the critical region is in agreement with the area law, indicating that even simple systems can support large amounts of quantum correlations. We study the scaling behavior of low-lying energy gaps for a restricted set of geometries, and find that even in this simplified case, it is impossible to predict the asymptotic behavior, with the data allowing equally good fits to exponential and power law decays. We can therefore, draw no conclusion as to the algorithmic complexity of a quantum adiabatic ground-state search for the system.

7 pages, 13 figures, final version (accepted for publication in PRA)

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Cited by in corpus (5)

• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• Evolution of Entanglement Entropy in One-Dimensional Systems
• Continuous unitary transformations and finite-size scaling exponents in the Lipkin-Meshkov-Glick model
• Entanglement and majorization in (1+1)-dimensional quantum systems
• Block Spin Density Matrix of the Inhomogeneous AKLT Model