Bipartite entanglement and entropic boundary law in lattice spin systems (10 pages)
By A. Hamma, R. Ionicioiu, Paolo Zanardi. 2004
208 citations recorded by the source corpus.
We investigate bipartite entanglement in spin-1/2 systems on a generic lattice. For states that are an equal superposition of elements of a group G of spin flips acting on the fully polarized state |0>{sup xn}, we find that the von Neumann entropy depends only on the boundary between the two subsystems A and B. These states are stabilized by the group G. A physical realization of such states is given by the ground state manifold of the Kitaev's model on a Riemann surface of genus g. For a square lattice, we find that the entropy of entanglement is bounded from above and below by functions linear in the perimeter of the subsystem A and is equal to the perimeter (up to an additive constant) when A is convex. The entropy of entanglement is shown to be related to the topological order of this model. Finally, we find that some of the ground states are absolutely entangled, i.e., no partition has zero entanglement. We also provide several examples for the square lattice.
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/78ba1af0fdc28740cc97ca203b346c575aefce93
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Citations in the corpus
- Measurement-driven entanglement transition in hybrid quantum circuits (2019, methodology): “As reviewed in Appendix A, the methodology involves following the dynamics of “stabilizers” – mutually commuting and independent Pauli string operators – that uniquely specify the wavefunction, and readily allow for calculation of the entanglement entropy [23, 32–34].”
- Quantum coherence and geometric quantum discord (2017, background): “(488) Let us point out that the “constant” term corresponds to the area law (Eisert et al., 2010; Hamma et al., 2005).”
- Prediction of Toric Code Topological Order from Rydberg Blockade (2020, background): “[20] Alioscia Hamma, Radu Ionicioiu, and Paolo Zanardi, “Bipartite entanglement and entropic boundary law in lattice spin systems,” Phys.”
- Topological Entanglement Entropy in Chern-Simons Theories and Quantum Hall Fluids (2008, background): “the ultra-deconfined limit of a Z2 gauge theory, a state with a vanishing correlation length, it is simple to compute the entropy [50, 14].”
- Space from Hilbert Space: Recovering Geometry from Bulk Entanglement (2016, background): “Our second example reconstructs a patch of the 2-d toric code [60], where it is possible to exactly calculate the entropy for different subregions [61].”
- Quantum Entanglement Growth Under Random Unitary Dynamics (2016, background): “This expression for the entanglement entropy has also appeared in [48, 49].”